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ELEMENTS OF LOGIC. 

IJV FOUR BOOKS. 



BOOK I Of the original of our ideas, 

their various divisions, and the manner 
in which they contribute to the in- 
crease of knowledge ; with a philoso- 
phical account of the rise, progress, 
and nature of human language. 

BOOK II Of the grounds of human 

judgment, the doctrine of propositions, 
their use in reasoning, and division in- 
to self-evident and demonstrable. 



BOOK III Of reasoning and demonstra 

tion, with their application to the inves- 
tigation of knowledge, and the comm»n 
affairs of life. 

BOOK IV..~.Of the methods of invention 
and science, where the several degrees 
of evidence are examined, the notion 
of certainty is fixed and stated, and the 
parts of knowledge in which it may be 
attained, demonstrated at large. 



DESIGNED PARTICULARLY FOR 

YOUNG GENTLEMEN AT THE UNIVERSlTi. 

AND TO PREPARE THE WAY TO THE STUDY OF PHILOSOPHY 
AND THE MATHEMATICS. 



BY WILLIAM DUNCAN, 

Professor of Philosophy 171 Marishal College, Aberdeen ^ 



Doctrina sed vim promovet insitam ; 

Rectique cultus pectora roborant Ho^v^'Vc ^:^ 



NEW-YORK: 



rUBLISHED BY EVERT DUYCKINCK, 

NO. 68, WATER-STREET. 

y. Van Riper. ...Pi inter. 




1818. 



J 






TO THE 

RIGHT HONORABLE 

STEPHEN POYNTZ, ESa 

Sir, 

If I take this opportunity of publishing to 
the world the esteem I have for a character to 
which learning is so greatly indebted, I hope you 
will not think yourself injured by such a decla- 
ration from a man that honors you, and who looks 
upon the liberty of putting the following work 
under your patronage, as one of the happy in- 
cidents of his life. 

From the first moment I formed the design of 
it, I had it in my thoughts to address it to you ; 
and, indeed, what could be more natural, than 
that I should be ambitious of inscribing a trea- 
tise upon the elements of philosophy, to one, 
w^ho has so eminently distinguished himself by 
his extensive knowledge in that, as well as all 
the other branches of human learning ? 

Your great abilities in every kind, have de- 
servedly recommended you to the notice of your 
king and country, and occasioned your being 
courted and importuned to accept of those high 
offices of state, which others pursue with so 
much eagerness, and find it often difficult to ob- 
tain, by all the arts and endeavors of ambition. 
Nor have your talents been confined to the view 
of your country alone. Foreign nations have 
seen and admired you, and still speak with the 
greatest applauses of your wise and able con- 
duct, when it was your province to act as a Bri- 
tish minister abroad. 



4 DEDICATION. 

But the qualities of a great statesman are not 
those alone by which you have rendered yourself 
illustrious. The virtues of private life no less 
actuate and adorn your whole behavior, and add 
a new dignity to the high station to which your 
merit has raised you. Affability, complacency 
of manners, and, above all, an extensive hu- 
manity and benevolence, which takes pleasure in 
doing good, are distinguishing parts of your 
character, and have contributed no less than your 
other extraordinary endowments, to that univer- 
sal acknowledgment which is paid you by your 
country. 

That you may long live to be an ornament and 
blessing to the nation, and to enjoy the pleasure 
which arises frnm a consciousness of the esteera 
and approbation of all good mefl, is the sincere 
and hearty prayer of. 

Sir, 
Your most obliged, and most obedient 
Humble Sei^s^ant, 

W. DUNCAN. 



INTRODUCTION, 



Sec. I.... Importance of the Knowledge o^ Ourselves. 

Of all the human sciences, that concerning man is 
certainly the most worth}'- of man, and the most neces- 
sary part of knowledge. We find ourselves in this 
world surrounded with a variety of objects : we have 
powers and faculties fitted to deal with them, and are 
happy or miserable in proportion as we know how to 
frame a right judgment of things, and shape our actions 
agreeably to the circumstances in which we are placed. 
No study, therefore, is more important than that which 
introduces us to the knowledge of ourselves. Hereby 
we become acquainted with the extent and capacity of 
the human mind ; and learning to distinguish what ob- 
jects it is suited to, and in what manner it must proceed 
in order to compass its ends, we arrive by degrees, at 
that justness and truth of understanding, which is the 
great perfection of a rational being. 

Sec. ii.... Different gradations of Perfection in Things, 

If we look attentively into things, and survey them 
in their full extent, we see them rising one above an- 
other in various degrees of eminence. Among the in- 
animate parts of matter, some exhibit nothing worthy 
our attention : their parts seem as it were jumbled to- 
gether by mere chance, nor can we discover any beau- 
ty, order, or regularity in their composition. In others, 
we discern the finest arrangement, and a certain ele- 
gance of contexture, that makes us affix to them a no- 
tion of worth and excellence. Thus metals, and pre- 
cious stones, are conceived as far surpassing those un- 
formed masses of earth, that lie every where exposed 
to view. If we trace nature onward, and pursue her 
through the vegetable and animal kingdoms, we find 
her still multiplying her perfections, and rising, by a 
just gradation, from mere mechanism to perception, and 
'from perception, in all its various degrees, to reason and 
understanding. 

A 2 



e INTRODUCTION. 

Sec. III.,.. Usefulness of Culture ^ and particularly of 
the Study of Logic, 

But though reason be the boundary by which man is 
distinguished from the other creatures that surround him, 
yet we are far from finding it the same in all. Nor is this 
inequality to be wholly ascribed to the original make 
of men's minds, or the difference of their natural en- 
dowments. For if we look abroad into the several na- 
tions of the world, some are over-run with ignorance and 
barbarity ; others flourish in learning and the sciences ; 
and what is yet more remarkable, the same people have 
in different ages, been distinguished by these very op- 
posite characters. It is therefore by culture, and a due 
application of the powers of our minds, that we increase 
their capacity, and carry human reason to perfection. 
Where this method is followed, knowledge and strength 
of understanding never fail to ensue ; where it is neg- 
lected, we remain ignorant of our own worth ; and 
those latent qualities of the soul, by which she is fitted 
to survey this vast fabric of the world, to scan the hea- 
vens, and search into the causes of things, lie buried in 
darkness and obscurity. No part of knowledge, there- 
fore, yields a fairer prospect of improvement, than that 
which takes account of the understanding, examines its 
powers and faculties, and shows, the ways by which it 
comes to attain its various notions of things. This is 
properly the design oi Logic, which may be justly styled 
the history of the human mind, inasmuch as it traces the 
progress of our knowledge, from our first and simple 
perceptions, through all their different combinations, 
and all those numerous deductions that result from va- 
riously comparing them one with another. It is thus that 
we are let into the natural frame and contexture of our 
own minds, and learn in what manner we ought to con- 
duct our thoughts, in order to arrive at truth, and avoid 
error. We see how to build one discovery upon anoth- 
er, and, by preserving the chain of reasonings uniform 
and unbroken, to pursue the relations of things through 
all their labyrinths and windings, and at length exhibit 
them to the view of the soul, with all the advantages of 
light and conviction. 

Sec. IV.... Operations of the Mind, 

But as the understanding, in advancing from one part 
af knowledge to another, proceeds by a just gradation. 
and exerts various acts, according to the different prO' 



INTRODUCTION. 

gress it has made, logicians have been careful to note 
these several steps, and have distinguished them in their 
writings by the name of the operations of the mind. 
These they make four in number, and agreeably to that 
have divided the whole system of logic into four parts, 
in which these acts are severally explained, and the con- 
duct and procedure of the mind, in its diflferent stages 
of improvement, regulated by proper rules and obser- 
vations. Now, in order to judge how far logicians have 
followed nature, in this distinction of the powers of the 
miderstanding, let us take a short view of the mind, and 
the manner of its progress, according to the experience 
we have of it in ourselves, and see whither the chain 
of our own thoughts will without constraint lead us. 

Sec. y ....Perception. 

First, then, we find ourselves surrounded with a va- 
riety of objects, which, acting differently on our senses, 
convey distinct impressions into the mind, and thereby 
rouse the attention and notice of the understanding. 
By reflecting, too, on what passes within us, we become 
sensible of the operations of our own minds, and attend 
to them as a new set of impressions. But in all this 
there is only bare consciousness. The mind, without 
proceeding any farther, takes notice of the impressions 
that are made upon it, and views things in order as they 
present themselves one after another. This attention 
of the understanding to the objects acting upon it, 
whereby it becomes sensible of the impressions they 
make, is called, by logicians, j^^'^ception ; and the no- 
tices themselves, as they exist in the mind, and are there 
treasured up to be the materials of thinking and know- 
ledge, are distinguished by the name oi ideas. 

Sec. \i... .Judgment. 

But the mind does not always rest satisfied in the bare 
view and contemplation of its ideas. It is of a more ac- 
tive and busy nature, and likes to be assembling them 
together, and comparing them one with another. In 
this complicated view oi things it readily discerns, that 
some agree and others disagree, and joins or separates 
them according to this perception. Thus, upon com- 
paring the idea of two added to two, with the idea of 
four, we, at first glance, perceive their agreement, and 
thereupon pronounce that two and two are equal to four» 
Again, that white is not black, that five is less than se- 



8 INTROOTCTIOK. 

ven, are truths to which we immediately assent, as soon 
as we compare those ideas together. This is the first 
and simplest act of the mind, in determining the rela- 
tion of things, when, by a bare attention to its own 
ideas, comparing any two of them together, it can at 
once see how far they are connected or disjoined. The 
knowledge thence derived is called intuitive, as requi- 
ring no pains or examination ; and the act of the mind 
assembling its ideas together, and joining, or disjoining 
them, aocording to the result of its perceptions, is what 
logicians term judgment. 

Sec. vu.... Reasoning. 

Intuition affords the highest degree of certainty ; it 
breaks in with an irresistible light upon the understand- 
ing, and leaves no room for doubt or hesitation. Could we 
in all cases, by thus putting two ideas together, discern 
immediately their agreement or disagreement, we should 
be exempt from error and all its fatal consequences. 
But it so happens, that many of our ideas are of such a 
nature, that they cannot be thus examined in concert, 
or by any immediate application one to another ; and 
then it becomes necessary to find out some other ideas 
that will admit of this application, that by means of 
them we may discover the agreement or disagreement 
we search for. Thus the mind wanting to know the 
agreement or disagreement in extent between two en- 
closed fields, which it cannot so put together as to dis- 
cover their equality or inequality by an immediate com- 
parison, casts about for some intermediate idea, which, 
by being applied first to the one, and then to the other, 
will discover the relation it is in quest of. Accordingly 
it assumes some staled length, as a yard, &c. and mea- 
suring the fields one after the other, comes by that 
means to the knowledge of the agreement or disagree- 
ment in question. The intervening ideas made use of 
on these occasions, are called proofs ; and the exercise 
of the mind in finding them out, and applying them for 
the discovery of the truths it is in search of, is what we 
term reasoning. And here let it be observed, that the 
knowledge gained by reasoning is a deduction from our 
intuitive perceptions, and ultimately founded on them. 
Thus in the case before mentioned, having found l^y 
measuring, that one of the fields make three-score square 
yards, and the other only fifty-five, we thence conclude, 
that the first field is larger than the second. Here the 
1 wo first perceptions are plainly intuitive, and gained 



INTRODUCTION. 9 

by an immediate application of the measure of a yard 
to the two fields, one after another. The conclusion, 
though it produces no less certain knowledge, yet dif- 
fers from the others in this, that it is not obtained by an 
immediate comparison of the ideas contained in it, one 
with another, but is a deduction from the two preceding 
judgments, in which the ideas are severally compared 
with a third, and their relation thereby discovered. We 
see, therefore, that reasoning is a much more complicat- 
ed act of the mind than simple judgment, and necessa- 
rily presupposes it, as being ultimately founded on the 
perceptions thence gained, and implj'ing the various com- 
parisons of them one with another. This is the great 
exercise of the human faculties, and the chief instru- 
ment by which we push on our discoveries, and enlarge 
our knowledge. A quickness of mind to find out inter- 
mediate ideas, and apply them skilfully in determining 
the relations of things, is one of the principal distinc- 
tions among men, and that which give some so remark- 
able a superiority over others, that we are apt to look 
upon them as creatures of another species. 

Sec. viu..., Method, 

Thus far we have traced the progress of the mind in 
thinking, and seen it rising by natural and easy steps 
from its first and simple perceptions, to the exercise of 
its highest and most distinguishing faculty. Let us now 
view it in another light, as enriched with knowledge, 
and stored with a variety of discoveries, acquired by a 
due application of its natural powers. It is obvious to 
consider it in these circumstances, as taking a general 
survey of its whole stock of intellectual acquisitions, 
disposing them under certain heads and classes, and ty- 
ing them together, according to those connexions and 
dependencies it discerns between them. It often hap- 
pens, in carrying on our inquiries from subject to sub- 
ject, that we stumble upon unexpected truths, and are 
encountered by discoveries which our present train of 
thinking gave no prospect of bringing in our way. A 
man of clear apprehension, and distinct reason, who, 
after due search and examinatio/i, has mastered any 
part of knowledge, and even made important discove- 
ries in it, beyond what he at first expected, will not 
sufifer his thoughts to lie jumbled together in the same 
confused manner as chance offered them • he will be for 
combining them into a regular system, wnere their mu- 
tual dependence may be easily traced, and the parts 



1^ INTRODUCTION. 

^eem to grow one out of another. This is that opeya- 

tion of the mind, known by the name of disposition or 

y,, method, and comes in the last in order, according to the 

■^^ division of the logicians, as presupposing some tolera- 

' ' ble measure of knowledge, before it can have an oppor- 

, tunity of exerting itself in any extensive degree. 

'/ Sec. IX.... Perception and Judgment terms of a -nery e.x- 

tensive signification. 

VVe see, then, that this fourfold distinction of the 
powers of the mind, in perception, judgment, reason- 
ing, and disposition, as well as the order in which they 
are placed, have a real foundation in nature, and arise 
from the method and procedure of our own thoughts. 
It is true, there are many other actions and modifications 
of the understanding, besides those above mentioned, 
^i as believing, doubting, assenting, &c. but these are all 

' *5 ; implied in the act of reasoning, in the like manner, as 

> <^ comprehending, abstracting, remembering, may be re- 

ferred to the first operation of the mind, or perception. 
N r This will appear more fully in the sequel, when we 

s^ Gome to handle the several parts of logic separately : at 

present we shall content ourselves with this general ac- 
count of things ; only it seems necessary to observe, 
that perce2ytion and judgment, in the propriety of the 
^- English tongue, have a much more extensive significa- 

^ tion than logicians commonly allow them. We not on- 

ly perceive the ideas in our own minds, but we are said 
also to perceive their agreement or disagreement ; and 
5^ ^ hence arise the common phrases of intuitive percep- 

v^' '''' tions, perceptions of truth, and of the justness of argu- 

ments or proofs ; where it is manifest, that the word is 
applied not only to our judgments, but also to our rea- 
.-, ,_ sonings. In a word, whatever comes under the view of 

P^; ' the mind, so as to be distinctly represented and taken 

" "^ notice of, whether an idea, proposition, chain of rea- 

soning, or the order and connexion of things, is thereby 
rendered an object of perception, and gives employ- 
ment to this first and most simple of our faculties. In 
like manner, the wovdi, judgment, is seldom, in com- 
'^, mon discourse, conaued to obvious and self-evident 

^ trutlis.^ It rather signifies those conjectures and guesses 

7^ '' that we form, in cases which admit not of undoubted 

certainty, and where we are left to determine by com- 
N paring the various probabilities of things. Thus a man 

r^ of sagacity and penetration, who sees far into the hu- 

mours and passions of mankind, and seldom mistakes 



INTRODUCTION. « H 

ia the opinions he frames of characters and actions, is 
said to judge well, or think judiciously. For these rea- 
sons, it might not be improper to change the common 
names of the two first operations of the mind, calling 
the one simple apprehension, and the other intuition ; 
which two words seem better to express their nature, 
and the manner in which they are conversant about their 
several objects. This accuracy of distinguishing, where 
there is any the least difference, is in a peculiar manner 
necessary in a treatise of logic, as it is the professed 
design of that science, to teach us how to form clear 
and distinct notions of things, and thereby avoid being 
misled by their similitude or resemblance. 

Sec. X,.. .Logic divided into Four Paris. Its usefulness 
and Excellency. 

Having thus given a general idea of the four opera- 
tions of the mind, and traced their connexion and de- 
pendence upon one another, I would next observe, that 
in consequence of this division of the powers of the un- 
derstanding, logic is also divided into four parts, which 
treat severally of these acts, and give rules and direc- 
tions for their due conduct and regulation. The opera- 
tions themselves we have from nature ; but how to ex- 
ert them justly, and employ them with advantage in 
the search of truth, is a knowledoe that may be acquir- 
ed by study and observation. It is certain, that we 
meet with false reasonings as well as just. Some men 
are distinguished by an accuracy of thinking, and a 
happy talent of unravelling and throwing light upon the 
most obscure and intricate subjects. Others confound 
the easiest speculations ; their understandings seem to 
be formed awry, and they are incapable of either con- 
ceiving clearl}^ themselves, or making their thoughts in- 
telligible to others. If then we set ourselves carefully 
to observe what it is that makes the one succeed so well, 
and how the others come to miscarry, these remarks will 
furnish us with an art of the highest use and excellency 
in the conduct of life. Now this is the precise business 
of logic — to explain the nature of the human mind, and 
the proper manner of conducting its several powers, in 
order to the attainment of truth and knowledge. It lays 
open those errors and mistakes we are apt through inat- 
tentions to run into, and teaches us how to distinguish 
between truth, and what carries only the appearance of 
it. By this means, we gro^^ acquainted with the nature 
and force of the understanding, see what things lie with- 



IE , INTRODUCTION. 

in its reach, where we may attain certainty and demon- 
stration, and when we must be contented with bare 
probability. These considerations sufficiently evince 
the usefulness and benefit of this science, which ought 
to be established as the foundation and ground- work of 
all our other knowledge, if we really wish to succeed 
in our inquiries. But we shall now proceed to treat pf 
its parts separately, according to the division given of 
Itiem above. 



ELEMENTS OF LOGtC. 



BOOK I. 

Of Simple Apprehension, or Percepliot. 

CHAP. I. 

OF THE Or.IGIXAL OF OUR IDEAS. 
— 040— 

Sec I Simple Aijpi'ehensioii and Ideas. 

The Hist thing we observe, when we take a view of 
what passes within us, is that we are capable of re- 
ceving impressions from a variety of objects ; that 
distinct notices are thereby conveyed into the under- 
standing ; and that we are conscious of their being^ 
there. This attention of the mind to the objects acting 
upon it, is what we call simple apprehension^ and is, in 
fact, the mind itself taking a view of things, as repre- 
sented to it by its own consciousness. It is by this 
means that we come to be furnished with all those 
ideas about which our thoughts are employed. For be- 
ing sensible of the impressions made upon us, and at- 
tending to the perceptions they bring, v/e can renew 
them again upon occasion, even v/hen the objects that 
first produced them are removed. Now, our are 
nothing else but these renewed representations of what 
we have at any time perceived and felt, by means of 
which things are again brought under the view of the 
mind, and seem to have a kind of existence in it. It 
is true, we can upon many occasions combine our ideas 
variously together, and thereby form to ourselves re- 
presentations of things that never had an existence in 
nature, as wheii we fancy a centaur, or a golden moun- 
tain ; but it is still certain, that the original ideas, 
out of which these are made, are such as have been 
conveyed into the mind by some former in^pressions, 
B 



14 ELEMENTS OF LOGIC. 

It remains therefore to inquire how we come by our 
first notions and perceptions of things. Wh^ce does 
the understanding derive these original impressions and 
characters, which it can combine in so many different 
ways, and represent to itself under such infinite varie- 
ties ? To this I answer, that if we attend carefully to 
what passes in our minds, we shall observe two inlets of 
knowledge, from whence, as from two fountains, the un- 
derstanding is supplied with all the materials of think- 
ing. 

Sec. n,,.,Jlll our original Ideas derived either fiom 
Sensation i 

First, outward objects, acting upon our senses^ 
rouse in us a variety of perceptions, according to the 
different manner in which they affect us. It is thus, 
that we acquire ideas of light and darkness, heat and 
cold, sweet and bitter, and all those other impressions 
which we term sensible qualities. This great source 
and inlet of knowledge is commonly distinguished by 
the name of sensation, as comprehending all the notices 
conveyed into the mind, by impulse made upon the 
organs of sense. 

Sec. III.. ..Or Reflection. 

But these ideas, numerous as they are, are wholly 
derived to us from without : there is therefore yet 
another source of impressions, arising from the minds 
attention to its own acts, when, turning inwards upon 
itself, it takes a view of the perceptions that are lodg- 
ed there, and the various ways in which it employs it- 
self about them. For the ideas furnished by the senses, 
give the mind an opportunity of exerting its several 
powers ; and as all our thoughts, under whatever 
form they appear, are attended with consciousness, 
hence the impressions they leave, when we come to turn 
the eye of the soul upon them, enrich the understanding 
with a new set of perceptions, no less distinct than those 
conveyed in by the senses. Thus it is that we get ideas 
of thinking, doubting, believing, willing, &c. which 
are the different acts and workings of our minds, repre- 
sented to us by our own consciousness. This second 
source of ideas is called rc^ec^«07i, and evidently presup- 



ELEMENTS OF LOGIC. lo 

.poses sensation ; as the impressions it furnishes are only 
of the various powers of the understanding, employed 
about perceptions already in the mind. 

Sec. IV Rise cmd Progress of Human Knowledge. 

These considerations, if we duly attend to them, will 
give us a clear and distinct view of the natural proce- 
dure of the human intellect, in its advances to know- 
ledge. We can have no perception of the operations 
of our own minds, until they are exerted ; nor can they 
be exerted before the understanding is furnished with 
ideas about which to employ them : and as these ideas, 
that give the first employment to our faculties, are evi. 
dently the perceptions of sense, it is plain, that all our 
knowledge must begin here. This, then, is the first 
capacity of the human mind, that it is fitted to receive 
the impressions made upon it by outward objects affect- 
ing the senses ; which impressions, thus derived into 
the understanding, and there lodged, for the view of the 
soul, employ it in various acts of perceiving, remember- 
ing, considering, &c. all which are attended with an 
internal feeling and consciousness. And this leads us 
to the second step the mind takes in its progress to- 
wards knowledge, viz. that it can, by its own consci- 
ousness, represent to itself these its several workings 
and operations, and thereby furnish the understanding 
with a new stock of ideas. From these simple begin- 
nings, all our discoveries take their rise : for the mind, 
thus provided with its original characters and notices of 
things, has a power of combining, modifying, and ex- 
amining them in an infinite variety of lights, by which 
means it is enabled to enlarge the objects of its percep- 
tion, and finds itself possessed of an inexhaustible stock 
of -materials. It is in the various comparison of these 
ideas, according to such combinations of them as seen» 
best to suit its ends, that the understanding exerts it- 
self in the arts of judging and reasoning, by which the 
capacious mind of man pushes on its views of things, 
adds discovery to discovery, and often extends its 
thoughts beyond the utmost bounds of the universe. 
Thus we see, as it were, at one glance, the v/hole pro- 
gress of the soul, from the very first dawnings of per- 



lt» ELEMENTS or LOGIC. 

ception, till it reaches the perfection of human know- 
ledge ; nor shall we, among all its vast stock of disco- 
veries, or that infinite variety of conceptions 'whereof 
the3^consist, be able to find one original idea which is 
riot derived from sensation or reflection, or one com- 
plex idea v^-^hich is not made up of those original ones. 

Sec. v....Diiision of our Ideas into Simple and Complex. 
Having thus shown how the mind comes to be first 
furnished with ideas, we shall next proceed to the 
consideration of the ideas themselves, and endeavour 
to give such an account of them, as will best serve to 
explain their several appearances, and the manner in 
which they are formed. It is evident, from what has 
been said above, that they all fall naturally under 
these two heads : first, those original impressions that 
are conveyed into the mind by sensation and reflection, 
and which exist there, simple, uniform, and without 
any shadow of variety. Secondly, those more complex 
notions of things, that result from the various com- 
binations of our simple ideas, whether they are con- 
ceived to exist of themselves, in any particular subject, 
or are united and joined together by the mind enlarg- 
ing its conceptions of things, and pursuing the ends 
nnd purposes of knowledge. These two classes com- 
prehend our whole stock of ideas : and, when consi- 
dered separately, in that order wherein they most na- 
turally seem to offer themselves to our thoughts, will, 
I hope, give such a view of the conduct and manner 
of the mind, as may contlibute not a little to intro- 
duce us to an acquaintance with ourselves, and make 
uz sensible of the capacity and extent of the human 
intellect. We proceed, therefore, to a more particular 
account of this divition of our icTeaSo 

CHAP. II. 

OF SIMPLE IDEAS. 

Sec. I.... Simple Ideas what. 
The first class of our. ideas are those which I di^- 
■in<TiiiL-:h by the name of simp-e pf:rc<^ption : be 



ELEMENTS OF LOGIC. 17 

cause they exist in the mind under one uniform appear- 
ance without variety or composition. For though ex- 
ternal objects convey at once into the understanding 
many different ideas, all united together, and making 
as it were one whole ; yet the impressions themselves are 
evidentl}' distinct, and are conceived by the mind, each 
under a form peculiar to itself. Thus the ideas of co- 
lour, extension, and motion, may be taken in at one and 
the same time, from the same body ; j'et these three 
perceptions are as distinct in themselves, as if they all 
proceeded from different objects, or were exhibited to 
our notice at different times. We are therefore care- 
fully to distinguish ^ij^tween our simple and primitive 
conceptions, and those aifferent combinations of them, 
which are often suggested to the mind by single ob- 
jects acting upon it. The first constitute our original 
notices of things, and are not distinguishable into dif- 
ferent ideas, but enter by the senses simple and unmix- 
ed. They are also the materials, out of which all the 
others, how complex and complicated soever, are form- 
ed ; and therefore ought deservedly to be looked on as 
the foundation and groundwork of our knowledge. 

Sec. h Simple Ideas of Sensation. 

Now if we take a survey' of these ideas, and their 
several divisions and classes, we shall find them all sug- 
gested to us,'^fther by our senses, or the attention of 
the mind to what passes within itself. Thus our no- 
tices of the different qualities of bodies, are all of the 
kind we call simple ideas and may be reduced to five ge- 
neral heads, according to the several organs which are 
affected by them. Colours, &c. and sounds, are con- 
veyed in by the eyes and ears ; tastes and smells by the 
nose and palate ; and heat, cold, solidity, &c. by 'the 
touch. Besides these, there are others which make im- 
pressions on several of our senses, as extension, figure, 
rest, and motion, &c, the ideas of which we receive 
into our minds both by seeing and feeling. 

Sec. Ill Simple Ideas of ReflexioUy^, 

ifwe next turn our view upon what passes within 
ourselves, we shall find another set of simple ideas ari-. 
B 2 



lb ELEMENTS OF LOGIC. 

sing from our consciousness of the acts and operations 
of our own minds. Perception or thinking", and voli- 
tion or willing, are what every man experiences inhim-^ 
self, and cannot avoid being sensible of. I shall only 
observe further, that besides all the above-mentioned 
perceptions, there are others that come into our minds 
by all the ways of sensation and reflexion ; such are the 
ideas of pleasure and pain, power, existence, unity, suc- 
cession, &c.. which are derived into'our understandings 
both by the action of objects without us^^and the con- 
sciousness of what we feel within. It is true some of 
these ideas, as of extension and duration, cannot be con- 
ceived altogether without partes, nevertheless, they are 
justly ranked among our simple ideas ; because their 
parts being all of the same kind, and without the mix- 
ture of any other idea, neither of them can be resolved 
into two distinct and separate conceptions. Thus they 
still answer the definition given above, of being one 
uniform appearance in the mind, with variety or plural- 
ity. But to prevent confounding our simple ideas of 
space and duration, with those complex modes of them 
marked out by the several measures commonly in use, 
as yards, miles, days, years, &c. it may perhaps be most 
proper to consider the least portions of either whereof 
we can form a clear and distinct perception, as the sim- 
ple ideas of that kind out of which all their other modes 
and combinations are formed. Such an instant, or 
point, may be conceived to be the same in respect of 
duration or space, as unity is in respect of numbers; 
and will serve best *to show, how by a continued addi- 
tion or repetition, our more enlarged and complex ideas 
are made up. 

Sec, IV.... Siinple Ideas have no Admission hut hy the: 
proper Inlets of Nature. 

Having thus given a general view of our simple 
^€eas, I have still two observations to make concerning 
ihem. The first is, that they are such as can only be 
conveyed into the mind by the proper channels and 
avenues provided by nature ; insomuch that if we are 
destitute of any of those inlets, by which the impres- 
sion? ^hat produce. -tbem are wont to be admitted, all the 



LLEMENTo «F LOGIC, 



() 



icieas thence arising- are absolutel}' lost to us; nor can 
tve, by any quickness of understanding, find a remedy 
for this want. A man born blind is incapable of tlie 
ideas of light and colours ; in like manner as one who 
fs deaf can form no notion or conception of sounds. 
Hence it appears, that these our simple ideas are just 
£uch as nature has furnished them, and have no depen^ 
dence on our will ; we can neither destroy them when 
in the understanding, nor fashion or invent any new 
one, not taken in by the ordinary means of perception. 
So that we here see the utmost bounds of human 
knowledge, which however mighty and enlarged, cai> 
not exceed the limits of those our simple original ideas, 
and their various coaibinations.. 

Sec. v.,.. They Jurnisk ample Materials of Knowledge^ 

And this leads me to the second observation I pro- 
posed to make, v.hich is, that though the mind cannot, 
in multiplying its conceptions of things, advance one 
step beyond the materials furnished it by sense and 
consciousness ; yet ?-s it has a pmver of combining, 
modifying, and. enlarging them, in. all the different 
ways in which they can be put together, it therefore 
finds itself in possession of an inexhaustible treasure 
of ideas, sufficient to employ it to the full extent of all 
its powers, and furnish matter for all those various 
opinions, fancies, and views of things, that make up 
the subject of its thoughts and contemplations. Let 
us but reflect upon the single idea of unity or one, and 
observe what a variety of combinations are formed, by 
continually adding it to itself; insomuch that the un- 
derstanding finds no stop or boundary, in its progress 
from number to number. In what an infinity of dif- 
ferent lights may extension alone be considered.; what 
limits can be set to that endless diversity of figures, 
which it is in the power of the imagination to fashion- 
and represent to itself ? if to .these we add those num- 
berless other combinations that result from variously 
compounding and comparing the rest of our simple 
ideas, we shall have little reason to complain of being, 
limited to ^ scanty measure of knowledge, or that the- 



20 . ELEMENTS OP LOGIC. 

excercise of the human faculties is confined within nar- 
row bounds. But having traced the progress of the 
mind thro' its original and simple ideas, until it begins 
to enlarge its conceptions by uniting and tying them 
together ; it is now time to take a survey of it as thus 
employed in multiplying its views, that we may see bj" 
what steps it advances from one degree of improve- 
ment to another, and how it contrives to manage that 
infinite stock of materials it finds itself possessed of. 

Sec. VI. ...The Division of complex Ideas into those of 
real Existence, and those framed by the Mind. 

Whoever attentively considers his own thoughts, 
and takes a view of the several complicated ideas that 
from time to time offer themselves to his understand- 
ing ; will readily observe, that many of them are 
such as have been derived from without, and suggest- 
ed by different objects affecting his perception ; others, 
again, are formed by the mind itself variously combi- 
ning its simple ideas, as seems best to answer those ends 
and purposes it has for the present in view. Of the 
fii'^st kind are all our ideas of substances, as of a man, a 
horse, a stone, gold. Of the second are those arbitrary 
collections of things, which we on many occasions put 
together, either for their usefulness in the commerce of 
life, or to further the pursuit of knowledge : such are 
our ideas of stated lengths, whether of duration or 
space ; as hours, months, miles, leagues, &c. which 
divisions are apparently the creatures of the mind, in- 
asmuch as w^e often find them different in different 
countries ; a sur€ sign that they are taken from no 
certain and invariable standard in nature. Many of 
our ideas of human actions may be also referred to 
this head; as treason, incest, manslaughter, &c. which 
complex notions we do not always derive from an actual 
view of what these words describe, but often from com- 
bining the circumstances of them in our minds, or, 
which is the most usual way, by hearing their names 
explained, and the ideas they stand for enumerated. 
These two classes comprehend all our complex con- 
ceptions, it being impossible to conceive any that are 



ELEMENTS OF LOGIC. ^1 



not either suggested to the understanding by some 
real existences, or formed by tlie mind itself arbitrarily 
uniting and compounding its ideas. AVc shall treat of 
each in order. 



CHAP. IIIv 

OP ouli Ideas or suBSTANclis. 

Sec. 1..., Ideas of Substances^ Collections of Simple 
Ideas, held together by some vnhwwn support. 

The first head of complex ideas mentioned in the 
ioregoing chapter, is that of substances, which I 
cheese to handle before the other ; because, as will af- 
terwards appear, the notices derived from this source 
very much help us in forming those arbitrary colles- 
lions, which make up4he second division. For fn many 
of them we take our hints from the reality of things, 
and combine ideas that actually exist together, though 
often with an exclusion of others, as will l^e explaii^^ed 
when we come to treat of abstract and universal notions 
It has been already observed, that the impressions con- 
veyed into the understanding from external objects, con- 
sist for the most part of manj' different ideas joined to- 
gether, which all unite to make up one whole. These 
collections of various ideas, thus co-existiiig in the same 
common subject, and held together by some unknown 
bond of union, have been distinguished by the name 9^ 
substances, a word which implies their subsisting of 
themselves, without dependence (at least as Ijr as oui* 
knowledge reaches) on anj' other created beings. Such 
are the ideas we have of «"ol^, iron, water, a man, ^c. 
For if we fix upon aqy oi.ie of these, for instance, golq, 
the notion under which we represent it to ourselves is 
that of a body yellow, very weighty, hard, fusible, mal- 
leable, «$<:c. w here we maj- observe, that the several pro- 
perties that go to the composition of gold, are rep- 
resented to us by clear and evident perceptions ; thie 
union too of these properties, and their thereby consti- 
tuting a distinct species of bodvj it clearly apprehend- 



22 ELEMENTS OF LOGIC. 

ed by the mind ; but when we would push our inqui- 
ries farther, and known wherein this union consists, 
what holds the properties together, and gives them 
their self-subsistence, here we find ourselves at a loss. 
However as we cannot conceive qualities, without at 
the same time supposing some subject in which they 
adhere, hence we are naturally led to form the notion 
of a support which, serving as a foundation for the co- 
existence and union of the different properties of things, 
gives them that separate and independent existence 
under which they are represented to our conception. 
This support we denote by the name, substance ; and as 
it is an idea applicable to all the different combinations 
of qualities that exist any whereby themselves, they are 
accordingly all called substances. Thus a house, a bowl, 
a stone, &.c. having each their distinguishing properties 
and being conceived to exist independent one of ano- 
ther, the idea of substance belongs alike to them all. 

Sec. u....The division of Modes into Essential and 
Accidental . 

In substances, therefore, there are two things to be 
considered : first, the general notion of self-subsist- 
ence, which, as I have said, belongs equally to them all ; 
and then the several qualities, or properties, by which 
the different kinds and individuals are distinguished 
one from another. These qualities are otherwise cal- 
led modes, and have been distinguished into essential 
and accidental, according as they are perceived to be 
separable or inseparable from the subject to which they 
belong. Extension and solidity are essential modes of 
a stone ; because it cannot be conceived without them ; 
but roundness is only an accidental mode ; as a stone 
may exist under any shape or figure, and yet still re- 
tain its nature and other properties^ 
Sec. in..., The Notion of Self subsistence inseparable 
from Subsistence. 

1 might run farther into these divisions and subdivi- 
sions, in which logicians have been very fertile ; but 
as they tend little to the advancement of real know- 
ledge, and serve rather to fill the memory with words 



ELEMENTS Or LOGIC; 23 

and their significations, than furnish clear and distinct 
apprehensions of things, I shall not trouble the reader 
with them. It is more mateiial to observe, that the 
change of properties in any substance, tho it oft-times 
changes the nature of that substance, that is, its spe- 
cies or kind ; yet it never destroys the general notion 
of self-existence, but leaves that equally clear and ap- 
plicable, as before any such alteration happened. Wood 
by the application of fire is turned into charcoal ; but 
charcoal, however different from wood is still a sub- 
stance, in like manner, wax may be converted into 
flame and smoke ; a human body will moulder into 
dust : yet these alterations destroy not their being or 
existence : they are still substancec as before, tho' un- 
der a different form and appearance. In the several ex- 
periments made by chemists, bodies undergo many 
changes, and put on successively a great variety of dif- 
ferent shapes, and yet, by the skill and address of the 
operator, they are often brought back to their first 
and primitive form. What alteration can we suppose 
the fire, or the application of any other body, to make 
unless on the configuration, texture, or cohesion of the 
minute parts ? when these are changed, the body is 
proportionably changed ; when they return to their 
original state, the body likewise puts on its first and 
natural appearance. 

Sec. IV.. », Foundation of the different l^ectes of Corpo- 
real Substances. 

All that is essential to matter, therefore, is the cohe- 
sion ofsolid extended parts : but as these parts are ca- 
pable of innumerable configurations — as their texture 
may be very various, and the internal constitution 
thence arising be of consequence extremely different in 
different bodies — we may from these considerations 
conceive pretty clearly the source and foundation of ail 
the different species of corporeal substances. Nor is 
this a notion taken up at random, or one of those chi- 
merical fancies in philosophy, derived rather from a 
w^armth and liveliness of imagination, than observa- 
tions drawn from things themselves. Do we not daily 



24 ELEMENTS OF LOGIC. 

see our food, by the changes it undergoes in the differ 
ent avenues of the body, converted first into blood, and 
tuence employed in nourishing, building up, and en- 
larging, the several parts of that wonderful fabric ? 
Rain, descending from the clouds, and ijiixing with the 
mould or earth of a garden, becomes aliment for trees of 
various kinds, puts on a diversity of forms, according to 
the different channels and conveyances through which 
it passes : and at last, after innumerable changes and 
transmutations, sprouts forth in leaves, opens in buds, 
or is converted into the substance of the tree itself.^ 
Can we conceive any greater difference between the 
component parts of gold, and those of stone, than be- 
tween the moistened particlesof garden mould, and those 
new forms and figures under which they appear, after 
they have been thus fashioned by nature for the pur- 
poses of growth and nourishment ? 

Sec. V.,.. Essence of Substances nothing hut the inter- 
nal structure and constitution ; 

Ifthi^beduly attended to, it will not appear won- 
derful to assert, that the variety of material substances 
arises wholly from the different configuration, size, tex- 
ture, and motion of the minute parts. As these happen 
to be variously combined, and knit together, under dif- 
ferent forms, bodies put on a diversity of appearances, 
and convey into the mind by tl?e senses all those seve- 
ral impressions, by which they are distinguished one 
from another. This internal constitution or structure 
of parts from whicH the several properties that dis- 
tinguish any substance flow, is called the essence of 
that substance, and is, in fact, unknown to us, any 
farther, than by the perceivable impressions it makes 
upon the oigans of sense. Gold, as has been said, is.a 
body yellow, very weighty, hard, fusible, malleable, 
&e. That inward structure, and conformation of its 
minute particles, by which they are so closely linked 
together, and from which the properties above men- 
tioned are conceived to flow, is celied its essence ; and 
the properties themselves are the perceivable marks that 
make it known to us, and distinguish it from all other 



ELEMENTS OF LOGIC. " 25 

subslunces ; for our senses are not acute enough to 
reach its inward texture and constitution. The parts 
themselves, as well as their arrangement, lie far be- 
yond the utmost penetration of human sight, even 
when assisted by microscopes, and all the other contri- 
vances of art. 

Sec. VI Is wholly unknown to usy and serves to distin- 
guish the Species ; 
Thus, as to the essence or internal constitution of 
gold, we are wholly in the dark ; but many of the pro- 
perties derived from this essence, make obvious and 
distinct impressions, as the weight, hardness, and yel- 
low colour, Lc These properties combined together, 
and conceived as co-existing in the same common sub- 
ject, make up our complex idea of gold. The same 
may be said of all the other species of corporeal sub- 
stances, as lead, glass, water, &c. our ideas of them 
being nothing else but a collection of the ordinary qua- 
lities observed in them. 

Sec. VII Yet it is rightly presumed to be distinct in 

all the several kinds. 
This, however, ought to be observed, that though 
the essence or inward structure of bodies is altogether 
unknown to us, yet we rightly judge, that in all the 
several species, the essences are distinct. For each spe- 
cies being a collection of properties, which, taken to- 
gether, are different from those of every other species, 
the conformation of parts, on which these properties 
depend, must in like manner be different ; and this, as 
we have said, constitutes the essence. Iron and glass 
are evidently distinct kinds of body ; their perceivable 
qualities have little or nothing common ; and there- 
fore the inward structure or constitution from which 
these qualities flow, cannot be the same in both. But 
after all, this is the only thing we can with certainty 
afiirm concerning these essences, which lying so wholly 
in the dark, v/e shall do well to lay them aside in our 
<-easonings about things, and adhere to those more in- 
telligible and settled ideas acquired by joining toge- 
ther their various properties and nowers. For thu^> 
V 



26 ' ELEMENTS OF LOGIC^ 

only is true knowledge promoted, when we argue from 
known qualities, and not from a supposed internal con- 
stitution, which, however real in itself, yet comes no* 
within the reach of our faculties, and therefore can 
never be a ground to us for any discoreries or im- 
provements. 

Sec. viir By what steps we arrive at ike Notions of 

Immaterial Substances. 
. Material substance, as I have said, includes the ides 
of solid, cohering, extended parts, and is divided into 
different classes according to the differed impressionis 
made upon the organs of sense. But, besides these 
sensible ideas recer\'ed from without, we also experience 
in ourselves thinking and volition. These actions have 
no connexion with the known properties of body ; nay, 
they seem plainly inconsistent with some of its most 
essential qualities. For the mind not only discovers 
no relation between thinking, and the motion or ar- 
rangement of parts ; but it also perceives., that conscious- 
ness, a simple individual act can never proceed from 
a compo»nde(^ substance, capable of being divided ro- 
to many. Let us suppose, for instance, a system of 
.matter endowed with thought ; then either all the 
parts, of which this system is composed, must think, 
which would make it not one, but a multitude of dis- 
tinct conscious beings ; or its power of thinking mu&t 
arise from the connexion of the parts one with another, 
Iheir motion and dispos-itiop, &L€. which, all taken to- 
gether, contribute to the production of thought. But 
it is evident, that the motion of parts, and manner of 
combining them, can produce nothing but an artful 
structure, and various modes of motion. All machines 
of human composition, as watclies, clocks, &.c. how- 
ever artfully their parts are set togethej, however com- 
plicated their structure — -though we conceive innume- 
lable diflferent motions, variously conjoined, and run- 
ning one into another with an endless diversity, yet 
Bever produce any thing but figure and motion. If a 
clock tells the hour and minute of the day, it is offly 
by the motion of the different hands, pointing succes- 
sively at the figures marked on the hour plate for that 
purpose. We never imagine thts to be the effect of 



ELEMENTS OP LOGIC^ 27 

Thought or intelligence ; nor conceive it possible, by 
Any refinement of structure, so to improve the compo- 
sition, as that it shall become capable oi knowJeuge and 
consciousness. The reason is plain : thought is some- 
thing altogether diflerentfrom moiion and f;gure ; thete 
U not the least conaexion betv.etn them , aud therefore 
it can never be supposed to result from them. 

Sec IX Which zve otherrvise call Sp:r its. 

This then being evident, that intelligence cannot 
arise from an union or combination of unintelligible 
parts ; if we suppose it to belong t<- any system of mat- 
ter, we must necessarily attribute it to all the parts, 
of which that «;)^stem is compo.^..d ; whereby, instead of 
one, we sliall, as was before obsen'ed. ftave a multi- 
tude of distinct conscious beings. And because mat- 
ter, how far soever we p'Tsue the mlnutoness of its 
pans, 15 sti!l capable of roptatcd divisions, even to in- 
finivy ; li is plr.in, that this absurdity wiil follow us, 
through all ^he suppositions that mske thought inherent 
in a material substance. Finding, therefore, conscious- 
ness iiiCOuipat'bie with the cohesion of solid separable 
parls W'^ lire n '--.^s-^.ri'y led to place it in some other 
substance, of a distinct nature and properties, which we 
call spirit. 

Sec. :^,.,,.Body and Spirit distinct Snbstajzces. 

And here it is carefully to be observed, that the se- 
veral species of corporeal substances, though distin- 
guished one from another, and ranked under different: 
names ; j^et, agreeing in some common properties 
which, taken together, make up the notion of body, 
are thence all conceived to partake of this general na- 
ture, and to differ only as different moditications of 
the sanre substance. Whatever consists of solid ex- 
tended parts, is called matter ; and as all the various 
species of body, however distinguished from one ano- 
ther by their several properties, have yet this in com- 
mon, that they are. made up of such solid separable 
parts, hence they fall naturally under the general de- 
nomination of material beings, and are not conceived to 
idiffer, but in their form. Thus gold, antimony, wood, 
kr. alike partake of the notion of bodv ; they are a;! 



"^o ELEMENTS O? LOGIC. 

equalty material substances, and have no other differ^ 
nice, but what arises from the different stracture and 
conformation, &c. of parts, as we have shown above. 
But spirit is something altogether distinct from body, 
nay, and commonly placed in opposition to it ; for 
which reason, the beings of this class are called imma- 
terial ; a word that implies not any thing of their na- 
ture, but merely denotes its contrariety to that of matter. 

Sec. XI,,,.. The re may he many various Species of Suh-- 
stances, besides those that come "within the reach ofou/n-^ 

Faci,,ltics, 

Bcdy and spirit, thei-efore, difter not as species of the 
same substance, but are really distinct kinds of sub- 
stances, and serve as general heads 'under which to 
rank all the particular beings that fall within the com- 
pass of our knowledge. For we having no ways of per- 
ception but sense and consciousness, can have no no* 
tices of things, but as derived from these two inlets. 
By our senses we are informed of the existence of so- 
lid extended substances ; and reflection tells us, that 
there are thinking conscious ones. Beyond these our 
conceptions reach not ; and therefore, though there may 
be many oJJier kinds, as different from them as they are 
from one another, yet having no faculties suited to 
them, th€y are as remote from our knowledge, as light 
and colours from the apprehension of a man born blind. 
I believe it will hardly be doubted but the substance 
of the Creator difiers more from that of his creatures, 
than any two created substances can from one ano^ 
ther ; and therefore when we call God a spirit, we 
ought not rashly to presume, that he is so in the same 
sense in which the human soul is a spirit. The word 
is, indeed, used by us, to denote in general all thinking 
intelligent substances, in which sense God is very fitly 
called a spirit. But it were the height of folly to ima- 
gine, because this name is applied as well to the mind 
of maD as the Creator, that therefore they partake of 
one common nature, and differ only as different modifi- 
cations of the same substance. This I mention here, 
to check the presumption of the human mind, always 
forward to conclude, that every thing comes with!i> 



ELEMENTS OF LOGIC. 29 

itS^ reach, and to den}'" existence to whatever exceeds, 
the comprehension of its scanty and limited powers. 
Beings of a superior ckss may enjoy many ways of per- 
fection unknown to us, from which they receive no- 
tices as dilTerent from those in our minds, as the ideas 
we apply to spirit arc from the ideas we apply to bod}'. 
Solid and thiiiking beings are, it is true, the only ideas 
of substance that we are able to frame ; but this is np 
more an argument against the existence of other kinds, 
than the want of the ideas of light and colours in a 
blind man would be a good argument against the reali- 
ty or possibility of such perceptions. 
Sec. XII Difference in the manner of conceiving Cor- 
poreal and Spiritual Substances. 
Before I dismiss this subject, it may not be improper 
to take notice of a remarkable difference as to the man- 
ner of our conceiving corporeal and spiritual substan- 
ces. Those of the first kind convey themselves into 
the niind by impressions made upon the organs of sense ; 
and as these impressions are diftbrent in different bodies, 
the ideas they produce myst of course vary in propor- 
tion. Thus we get perceptions of distinct powers and 
properties, and range bodies into classes, according as 
we find them to agree or disagree in these their obser- 
vable qualities. But it is not so in our notion of spi- 
rits ; for having no conception of their powers and" 
operations but by what we feel and experience within 
ourselves, we camiot ascribe to them properties or ways 
of knowledge, distinct from those suggested to us by 
our own consciousness. And hence it is, that though 
we readily own there may be various ranks of spiritual 
beings, yet we are not to imagine them divided from 
^ne another by any diversity of powers -and operations, 
but merely by possessing the same powers, &c. in a 
higher or lower degree. It is not, however, repugnant 
to reason, that they should be distinguished by their se- 
veral properties in like manner as sensible things are 
by the different qualities observable in them ; but pro- 
perties of intellectual natures, distinct from those of our 
-own minds, being altogether remote from our concep- 
lioHj cannot serve as a means whereby to distinguish 
C 2 



30 ELEMENTS QP JLOGK:^ 

their different orders. We are, therefore, necessitated 
to conceive of them in a manner suited to our way of 
knowledge ; and when we would rank them into spe- 
cies, according to the degrees of superiority they are 
imagined to possess in the scale of being, we ascribe to 
them what we find most excellent in ourselves, as know- 
ledge, thinking, foresight, &c. and those in different 
measures proportioned to the station peculiar to each 
rank or species. But that this is a very imperfect waj^ 
©i distinguishing the various orders of intellectual be- 
ings, will not, I think, need many words to make it ap- 
pear ; especially if we cgnsider, that the manner of 
communicating their thoughts, without the interven- 
tion of bodily organs, is a thing to us altogether incom- 
prehensible, and necessarily leads us to suppose, that 
they have ways of perception and knowledge which our 
faculties cannot give us any notice of. 

Sec. xiii.,,.,XI^e hounds of Knowledge in our present 
state very narrow. 

But I shall not pursue these reflections farther ; what 
has been said sufficing to give us some little insight into 
the extent and capacity of our own minds 5 to convince 
!is that our present state will not admit of a perfect and 
adequate comprehension of things ; and to kt us see, 
that there may be other ways of knowledge, beyond the 
reach of the faculties we now enjoy ; which yet, in suc- 
ceeding stages of our existence, we may arrive at, when, 
being freed from the present cumbersome load of the 
body, we shall mount up to stations of greater eminence, 
and advance by a perpetual series of approaches towards 
him, who is the standard of perfection and happiness. 



CHAP. IV. 

OF IDEAS FRAMED BY THE JIIND,. 

■Beg. i....,hi Jraming many complex Ideas, the Mind i^ 
wholly active, aiid proceeds by a voluntary choice. 
Hitherto we have considered only such eombi-. 
riations of our simple ideas &s have a real unitvB 



ELEMENTS OF LOGIC. 31 

in nature, and are suggested to the mind by things 
themselves variously affecting our perception : it is now 
time to take a view of the other class of our complex 
notions; I mean those arbitrary collections of different 
ideas, which we on many occasions bring together by 
that power which we find in ourselves, of uniting, com- 
paring, and diversifying our notices of things. In the 
reception of simple ideas, and even in those ofsubstaa- 
ces, the understanding is wholly passive, and the per- 
ceptions produced correspond to the impressiotis made 
upon it. When we see a house, or a tree, they neces- 
sarily appear each under its proper form ; nor is it in 
our power to receive from these objects other ideas than 
what they are fitted to produce. But in this second 
class of complex conceptions, the mind acts voluntari- 
ly and of choice ; it combines only such ideas as are 
supposed best to suit its present purpose; and alters or 
change^ these combinations, by inserting some, and 
throwing- out others, according as the circumstances of 
things require their being viewed in different lights. 
Now as this is by far the most comprehensive branch of 
our ideas, and includes those that most frequently occur 
in the search and pursuit of knowledge, I shall endea- 
vour to treat them in the exactest order and method ; 
and for that purpose range them under several heads 
according to the different acts of the mind exerted in. 
framing and putting them together. 

Sec. u..^.. Three several Acts exerted by the Mind in 
framing its arbitrary Ideas, viz. Composition ; 

These acts may in the general all be reduced to three. 
3. Composition, when we join many simple ideas toge- 
ther, and consider them as one picture or representa- 
tion. Such are our ideas of beauty, gratitude, a fui»- 
long, &c. And here let it be observed, that the mind 
sometimes confines itself to the various considepation of 
the same idea, and, by enlarging it in different degrees, 
exhibits it under a diversity of forms. Thus by adding 
units together, in distinct separate collections, we 
come by the several combinations of numbers, as a 
dozen> a score, a million. At other times we unite 



- 32 ELEMENTS OF LOGIC. 

perceptions of different kinds ; in which case the com- 
position is more manifest, and the idea itself becomes oi 
course more complicated. Harmony, for instance, is a 
compound idea, made up of many different sounds 
tjnited ; all which the musician must have, and put to- 
l>ether in his mind, before the ear can be entertained 
with the actual performance. Now although the act of 
the mind is in some measure exerted in the frarhing; 
all our complex notions, yet aS many of them include 
certain limited and particular considerations, arising 
from other operations of the mind employed about 
them, it is necessary to take account of these acts also, 
if we would conceive clearly the manner in which the 
several species of our compound ideas are formed. 
Sec. Hi Mstraction. 

2. The next operation therefore of the mind, about its 
ideas, is abstraction, when we separate from any of our 
conceptions all those circumstances that render it parti- 
cular, or the representative of a single determinate 
object ; by which means, instead of standing for an in- 
dividual, it is made to denote a whole rank or class of 
things. Thus upon seeing, for instance, a square or 
circle, tve leave out the consideration of their bulk, 
and every thing else peculiar to them, as they imme- 
diately affect our sight, retaining only the notion of 
their figure and shape. In this manner we get our ge- 
neral ideas ; for such naked appearances, separated 
from the cfrcumstances of time, space, kc. serve the 
mind as standards by which to rank and denominate 
particular objects. When therefore we meet with a 
figure answering to that shape and form we had laid 
■up in our understandings, it is immediately referred by 
the mind to this pattern, and called by its name, 
which by this means becomes proper to the whole 
species. Thus a square, or circle, are universal terms, 
common to all figures of that particular shape, and 
alike applicable to them wherever they exist; in like 
manner as the ideas themselves are general, and repre = 
sentatives of all the jiind. 

Sec. IV And Comparison, 

o. The third and last act of the oiiad about its idea?j 



ELEMENTS OF LOGIC. 33 

is the comparing them one with another, vvhftn we carry 
our consideration of things beyond the objects them- 
selves, and examine their respects and correspondences 
in reference to other things which the mind brings 
into view at the saone time. It is thus we get all our 
ideas of relations^ as of greater, less, older, j'ounger, 
father, son, and innumerable others. This threefold 
view of our ideas, as either compounded of many others 
put together, or made universal by the abstraction of 
the mind, or as representing the various relations and 
habitudes of things, will give us an opportunity of ob- 
serving whatever is most curious and useful in this 
fundamental branch of knowledge, and of explaining 
^the manner and procedure of the understanding in en- 
larging its views^ and multiplying the ojyects of per- 
ception. That we ma}' therefore conceive of this mat- 
ter with the greater order and clearness, we shall make 
each of these several ideas the subjectofa distinct article. 



ART. I. 

OF COMPOUND IDEAS. 

Sec. I Compound Ideas considered here merely as 

Combinations of ike Understanding. 
We begin therefore with those ideas which may 
be properly termed compound^ as being derived from 
that power the mind has of uniting many conceptions 
iHto one. Though this class comprehends, in some 
sort, all our complex notions, yet they are at present 
considered merely as they are combinations of the un- 
derstanding, and with a view to those particular ideas* 
out of which ihey are framed. Here, as was already 
observed, the mind sometimes proceeds by enlarging 
and diversifying the same idea ; at other times it brings 
together ideas of different kinds ; and in both ways 
finds infinite scope and variety. But that we may fol- 
low the natural procedure of the intellect, and trace it in 
its advances from simple to more complicated acts, 
vz shall first take a view of it as employed about one 



34 ELEMENTS OF LOGIC. 

£nd the s^tne idea, where perhaps we may meet witl^ 
such instances of address, management, and contri- 
vance, as will appear perfectly astonishing to one who 
has never set himself seriously to consider the manner 
and conduct of his own mind. 

&£€. ii...^Mniiy the Original and Foundation of all our 
Ideas of Number. 
The most obvious and simple idea we have, is that of 
unity or one. By adding it to itself continually, and re- 
taining the several collections in our minds, we come 
by ali the different combinations of numbers, in which 
we readily perceive an endless diversity. All these 
ideas are nevertheless evidently distinct among them- 
.selves, the addition of a single unit constituting a 
immber as clearly different from that immediately be- 
fore it, as any two the most remote ideas are from one 
another. But that the understanding may not lose it- 
self in the consideration of those infinite combinations 
of which u!iity is capable, it praceeds by regular steps ; 
and beginning with the original idea itself, pursues it 
through all its varieties, as they are formed by the re- 
peated continual addition of unit after unit. Thus 
numbers are made to follow one another in an orderly- 
progression, and the several successive collections are 
distinguished by particular names. 

Sec. iu...,,The artfnl composition of the names ofKuiTi" 
hers a great help to our conceptions ; 
And here we ma}^ take notice of a wonderful artifice 
made use of by the mind, to facilitate and help it for- 
ward in its conceptions. For as the advance from num- 
ber to number is endless, were they all to be distinguish- 
ed by different denominations that had no connexion or 
dependence one upon- another, the multitude of them 
must soon overcharge the memory, and render it impos- 
sible for us to go any great way in the progress of num- 
bering. For this reason it is so contrived, that the 
change of names is restrained to a iG^'v of the first com- 
binations, all the rest that follow being marked by a 
repetition of the same terms, variously compounded and 
Jinked together- Thus tiiirleen is ten and three, fou?- 



ELEMENTS 07 LOGIC. 3^ 

teeji, ten and four^ and so on to twenty, or two ten?, 
when we begin again with one, two, &c. until we ad- 
vance to thirty, or three tens. In this manner the 
progression continues ; and when we arrive at ten tens, 
to prevent confusion by a too frequent repetition of 
the same word, that sum is distinguished by the name 
of a hundred. Again, ten hundred is called a thousand 
at which period the computation begins anew, running 
through all the former combinations, as ten thousand 
a hundred thousand, ten hundred thousand; which last 
collection, for the reasons mentioned above, has the 
name of a million appropriated to it. With this mil- 
lion we can begin as before, until it is repeated a mil- 
lion of times ; when, if we change the denomination 
to billions, and advance in the same manner through 
trillions, quartillians, the series may be carried on with- 
out confusion, to any length we please. 

Sec. IV And of the principal Reasons that our Ideas 

of Numbers are so remarkably distinct. 

This artful combination of names to mark the gra- 
dual increase of numbers, is perhaps one of the greatest 
refinements of the human understanding, and particu- 
larly deserves our admiration for the manner of the 
composition ; the several denominations being so con- 
trived as to distinguish exactly the stages of the pro- 
gression, and point out the distance from the begin- 
ning of the series. By this means it happens, that our 
ideas of numbers are of all others the most accurate 
and distinct ; nor does the multitude of units assem- 
bled together, in the least puzzle or confound the un- 
derstanding. It is indeed amazing, that the mind of 
man, so limited and narrow in its views, should yet 
here seem to shake ofif its natural weakness, and disco- 
ver a capacity of managing with ease the most bulky 
and formidable collections. If we inquire particular- 
ly into the reason of this, we shall find it wholly owing 
to the address of the mind in thu3 distinguishing num- 
bers- by diflferent names, according to the natural or- 
der of progression. For as those names are made to 
grow oae s>«t of another, they may be aptly compared 



3-6 ELE5IENTS OF LOGIC. 

to a chain, ail whose parts are linked tog;ether by an 
obvious and visible connexion. Hence it comes to pass 
that when we fix our thoughts upon any number, how- 
ever great and seemingly unmanageable; yet, if it i& 
once determined to a p^irticular name, we find it easy 
to run back through all the stages of the progression, 
even till we arrive at unity itself. By this means we 
see, with a single glance of our minds, not only the two 
extremes of the number under consideration, but also 
the several intermediate parts, as they are united to 
make up the whole. 

Sec. V As they help us to a clear Perception of the in- 

terjacent Parts. 

Now it is to this clear and accurate view of the in- 
terjacent ideas, that we owe our so distinct perception 
of the various combination of numbers. And indeed wc 
may observe, in the general, that all our ideas of quan- 
tity, especially when they grow to be very large, are 
no otherwise ascertained than by that perception we 
have of the intervening parts, lying, if I may so say, 
between the extremes. When we look at any object 
considerably distant fronf^, if we have a clear view 
of the interjacent lands and houses, we are able to de- 
termine pretty nearly of its remoteness ; but if, with- 
out such a knowledge of the intervening spaces, we 
should pretend to judge of the distance of objects, as 
when we see the spire of a steeple behind a wall, or be- 
yond a mountain, every one's experience is a proof how 
liable we are, in these cases, to be deceived. Just so it 
is in judging of duration. When we carry back our 
thoughts to any past period of our lives, without con- 
sideration of the number of years or months, we find 
that our itiea of the time elapsed grows more distinct, 
in proportion as we become sensible of the intermedi- 
ate parts of our existence. At first we are apt to judge 
the distance extrem.ely short ; but when we set our- 
selves to consider our several successive thoughts and 
actions, the idea of the duration grows upon us, and 
continues to increase as the attention of the mind brings 
new periods dtf life into view. 



, t:LEMENTS OJ' LOGIC. 37 

* c. Vi...JVithout names, we cannot make any progress 

in Numbering, 
Hence it will be easy to conco*. e how much the mind 
is helped forward in its perception of number, by that 
ready comprehension of all the several stages in a pro* 
gression which peculiarly belongs to ideas of this class. 
But this, as I have before intimated, we derive from the 
orderly series and connexion of names, insomuch that 
where they cease, the computation of numbers also ceases 
with them. We caR have no idea of any sum, without 
a knowledg-e ef all the terms that go before, according* 
to the natural order in which tliey follow one another : 
so that he who cannot, in a regular way, count to nine- 
ty-nine, will never, while that incapacity continues, be 
able to form the idea of a hundre<i ; l^cause the chain 
that holds the parts togetl>er, is to him wholly unser- 
viceabk, nor can he represent to his mind the several 
interjacent combinations, without which it is impossi- 
ble in this case to arrive at a distinct perception. 

■Sec, vu....Th€ great advantages of Address in Class- 
ing our complex Conctptiojis-. 
T have insisted the more largely. upon this, not only 
because it is by number that we measure all other 
things, as duration, extension, motion, &c. but also 
because it lets us into the most natural view of the con- 
duct and procedure of the understanding, and makes us 
sensible of the great art and address that is necessary in 
the classing our very complex conceptions. He that can 
po put together the component parts of an idea, as that 
they shall lie obvious to the notice of the niind, and pre- 
sent themselves, when occasion requires, in a just and 
fjrderly connexion, will not find it very difficult to obtain 
clear and accurate perceptions, in most of those sub- 
jects about which our thoughts are conversant. For the 
great art of knowledge lies in managing with skill the 
capacity of the intellect, and contriving such helps as, 
if they strengthen not its natural powers, may yet ex- 
pose them to no unnecessary fatigue, by entangling and 
perplexing them with considerations remote from the 
business in hand. When ideas become very complex. 
D 



38 ELEMENTS OF LOGIC* 

and by the multiplicity of their parts grow too unwieldj^ 
to be dealt with in the lump, we must ease the view of 
the mind by taking them to pieces, and setting before 
it the several portions separately, one after another^ 
By this leisurely survey we are enabled to take in the 
whole ; and if we can draw it into such an orderly com- 
bination, as will naturally lead the attention, step by 
step, m any succeeding consideration of the same idea 3 
we shall ever have it at command, and with a single 
glance of thought be able to run over all its parts. I 
have therefore explained here, at some length, the con- 
duct of the mind in mimbering ; it seeming to me the 
best model in this kind, whether we consider the many 
advantages derived from such an orderly disposition of 
our ideas, or the ^reat art and skill displayed in binding 
Ihese ideas together* This also is farther remarkable 
in the consideration of number, that from it chiefly we 
derive the notion we have of infinity ; it being appar- 
ent, that, in adding number to number, there is no 
end ; the possibility of doubling or increasing our stock 
in any degree, remaining as obvious to the understand- 
ing, after a great and continued run of progressionSj 
as wlien it first began the Gomputationr 

?sc. viil.., .The Consideration ofNumher, of great Use 
in ascertaining our Ideas of Space and Duration. 

If we now turn our thoughts towards space and du- 
ration, here too we shall find that we very seldom ar- 
rive at clear and distinct ideas of either, but when we 
introduce the consideration of number. The more ob- 
vious and limited portions,- it is true, easil}' slide into 
the mind, in the natural way of perception ; but it 
was the necessity of comparing these together, that 
put us upon the contrivance of certain stated measures 
by which precisely to determine the quantity in each. 
Thus, incheSj feet, yards, miles, &c. ascertain our ideas 
of extension : as minutes, hours, days, years, &c. mea- 
sure the progress of duration. The lesser parts, as ly- 
ing most open to the notice of the understanding, and 
being more on a level with its powers, are retained 
with tolerable exactness ; and the larger portion?. 



ELEMENTS OF LOGIC. 39 

■when the number of repetitions of which they are 
made up is known, are thereby also reduced into clear 
and determinate conceptions. A foot, and yard, are 
measures easily comprehended by the mind ; nor do we 
find any difficulty in conceiving a mile, when we consi- 
der it -as equal to a certain number of yards. If we are 
still for increasing the standard, we may take the se- 
mi-diameter of the earth, and supposing it equal to 
8000 miles, make use of it as a measure by which to 
ascertain the distance of the sun or fixed stars. Just so 
it is in duration; from hours we rise to days, months, 
and years ; by these, repeated, and added together, 
we measure time past, or can run forward at pleasure 
into futurity, and that without any confusion or per- 
plexity. 

Sec. IX Wiihout they arc ajyt to degenerate into a con- 

/used and irregular Heap. 

It is however to nutliber alone that we owe this dis- 
tinctness of perception, inasmuch as fcpace and time, 
considered apart from the regular and orderly repeti- 
tion of miles or years, 'leave no determinate impres- 
sions in the mind, by which to know and distinguish 
their several portions. Ideas of either, thus taken in 
at a venture, are a confused and irregular heap, especi- 
ally where we endeavour to enlarge and magnify cur 
views, and give full play to the powers of our intel- 
lect. Something indeed the mind conceives, va^t and 
mighty, but nothing that is precise, accurate, and just. 
But when it begins to consider these ideas as made up 
of parts, and fixing upon such as are proportioned to 
its reach, sets itself to examine bow often they are re- 
peated to make up the whole, the perceptions of the un* 
derstanding put on a new form, and discover their ex- 
act bounds and limits. 

Sec. X Infinity an Object too mighty for the survey of 

the Human Mind. 

And thus, as before in number, so here in extension 

and duration, the mind begins with simple and obvious 

notices, advancing by degrees to more enlarged and 

intricate conceptions. A day. or a furlong, are of easy 



40 ELEMENTS/ OF LOGIC. 



apprehension to the understanding, and by their subdi 
visions into still lesser spaces,, exhibit themselves dis- 
tinctly in all their parts. With these variously re- 
peated, we travel through space and time ; so that be- 
ing able to reduce all our ideas of this class, however 
mighty and enlarged, to the clear and determinate per- 
ceptions of nilmber, we can conduct our thoughts with- 
out perplexity, ami never find ourselves p^^izled, but 
when, presuming too much on our own strength, we^ 
launch iato speculations, tbat stretch beyond the pow- 
ers of the human intellect. Number may be compared 
to a line, that, setting out from unity, runs on in a con- 
tinued increa€e of length, without a possibility of ever 
arriving at its ultimate period. So far as we pursue it 
in our thoughts, and trace its regular advances, so far 
our ideas are accurate and just. But when we let loose 
our understandings, after a boundless remainder, and 
would fathom the depth of iafinit}?^, we find ourselves 
!ost am^idst the greatness of our own conceptions. 
Some notions, it is true, we have, but such as, exceed- 
ing the dimensions of the mind, lie involved in dark- 
ness and obscurity ; and being destitute of order, me- 
thod, and connexion^ afford no foundation whereon to 
build any just aud accurate conclusion.. 

Sec. xi......JVcr«r represented in its full dimensions, hui 

by an endless and eve^r growing Idea. 

And this perhaps may be tiie reasoa why many mo- 
dern philosophers, in their, discoui'ses concerning infi- 
nity, have run into apparent contradictions ; because, 
"Encountering an object too large for the survey of the 
understanding, they found themselves surrounded with 
inextricable difficulties, which their scanty and defec- 
tive ideas were by no means able to dissipate or remove. 
The truth of it is, finite ideas alone are proportioned 
to a finite understanding j and although we are not 
wholly without a notion of the infinity of number^ 
y^t it is not such a one as comprehends and exhausts 
its object, or exhibits it to the mind in its full size 
And dimensions. We only see the idea, as capable at 
ia endless increase, but cannot by any effort of thouglil 



ELEMENTS OF LOGIC. 41 

take in the whole prospect ; and indeed it is properly 
that part of it which lies beyond the reach of our per- 
ception, and still remains to be taken into the account, 
to which we give the name of infinity. 

Sec. XII Duration, 'whether considered as past or to 

come. Boundless, whence our Idea of Eternity. 
This idea of the infinity of number, imperfect as it 
may seem, is nevertheless that by which the mind as- 
cends to the conception oi eternity and immensity. For 
when we consider duration, either as past or to come, 
we find nothing to stop the progress of our thoughts, 
in the repetition of years, or millions of years : the 
farther w^e proceed, the more the idea grow s upon us ; 
and when we have wearied ourselves with vain efforts, 
we must own at last that we can no more arrive at the 
end of duration, than at the end of number. It. is 
true, the several generations of men rise and disappear 
in very quick successions ^ earth itself maj' decay ; and 
those bright luminaries that adorn the firmament of 
heaven, be extinguished. But the course of time will 
Hot be thereby disturbed ; that flows uniform and in- 
variable, nor is bounded by the period of their exist- 
ctTize. This double view of duration, as having already 
revolved through numberless ages, and yet still ad- 
vancing into futurity in an endless progression, pro- 
perly constitutes our ideas of eternity. We speak in- 
deed of an eternity past, an eternity to come, but 
both these are bounded at one extreme : the former 
terminates in the present moment, and therefore has an 
end : the latter sets out from the same period, and 
therefore has a beginning ; but, taken together, they 
form a line both ways infinitely extended, and which 
represents eternity in its full dimensions. 

.Sec. xiii The Idea of Immensity derivedfrom the Con- 
sideration of Space ever growing on all sides of us. 
As, in the consideration of time, we fix upon the 
present moment, regarding it as the middle point which 
divides the whole line of duration into two equal parts ; 
so, in the consideration of space, that particular place 
In which we exist is looked upon as a kind of centre to 



42 ELEMENTS OP LOGIC, 

the whole expansion. From thence we iel !oose our 
thoughts on every side — -above, below, around — ^and 
find we can travel on, in the repetition of miles, and 
millions of miles, without ever arriving at the end of the 
progression. It is not difficult, indeed, to carry our 
conceptions to the utmost bounds of the universe ; at 
least so far as it falls within our notice. But then the 
imagination rests not here ^ it sees immeasurable spaces 
beyond, capable of receiving new worlds, which it can 
pursue, as rising one above another in an endless suc- 
cession. This consideration of space ever growing on 
all sides of us, and yet never to be exhausted, is that 
which gives us the idea of immensity ; which is in fact 
nothing else but the infinity of number, applied to cer- 
tain portions of extension, as miles, or leagues, &c. 
and these conceived as extended every way around us^. 
in infinite and innumerable right lines. 

Sec. XIV Compound Ideas resulting' Jrom the Union 

of perceptions of different Kinds, 

Hitherto we have considered the mind as employed 
about one and the same idea, enlarging and diversify- 
ing it in various forms. We have seen it rising from 
the most simple and obvious notices to the e<>nception 
of infinity itself ; and taken a viq^y of it in all the dif- 
ferent stages of its improveriient. Let us now proceed 
lo the more complicated act of composition, when the 
inind brings several ideas of different kinds together, 
and voluntarily combines them into one complex con- 
ception. Such, for instance, is our idea of a tune^ as 
comprehending a variety of notes, with many differ- 
ent modulations of sound. And here it is to be observ- 
ed, that though the complex idea may be excited in us, 
by hearing the air itself struck off upon a proper in- 
strument ; yet, considered originally, it still belongs 
to this class of perceptions, which are distinguished as 
the arbitrary collections of the mind. It was the mu- 
sician, or composer, that combined the several notes » 
and determined the order in which they were to follow 
one another ; nor had that peculiar composition of 
sounds any real union in nature j before they were thus 



ELEMENTS OF LOGIC. 43 

brought together in his mind. Of the same nature ar* 
most of our ideas of human actions ; for thougli many 
of them come to our notice by seeing the actions them- 
selves, or hearing them described by others, as diatil- 
Utigy curving, treason^ k.c. yet it is plaiti that they must 
.have been projected and contrived in the mind of man 
before they had a real existence. 

Sec. XV,. ..How the Mind is determined in making these 
Combinations. 

It is here that the understanding has the greatest 
scope, and finds most employment for its active powers : 
nor indeed is it possible to set any bounds to the ideas 
of this class ; the combinations already made being al- 
most innumerable, and those j^et in the power of the 

,mind aflbrding an endless diversity. It may not, how- 
ever, be amiss to consider how w^e conduct ourselves 
amidst so great a variet}'-, and by what rules we pro- 
ceed in making those combinations to which we have 
affixed particular names, while others, perhaps, no less 
obvious, are neglected. The idea of killing, for in- 
stance, joined to that of a father, makes a distinct spe- 
cies of action, known by the name o( parricide. It was 
doubtless as obvious to distinguish between the killing- 
of an old man and a child, which yet we find is not done ; 
both these actions being comprehended under the ge*- 

.neral name of murder. By what views therefore does the 
mind regulate its combinations ? Why is it determined 
to one collection of ideas rather than another ? This 
cannot be well understood, without observing, that it 
is the end of language to communicate our thoughts 
one to another. Words aie the signs of our ideas, and 
-:erve to express the conception of the mind. Now it is 
apparent, that such conceptions as are most apt to occur 
in the commerce of life, would be first distinguished by 
particular names ; the frequent occasion men have, of 
mentioning these among themselves, rendering this ab- 
solutely necessary. But as many of these conceptions 
are collections of dilTerent simple ideas, hence we are 
insensibly led to such peculiar combinations, as are 
most serviceable to purposes of mutual intercourse and. 
communication. 



44 ELEMENTS OP LOGIC, 



Sec. XVI..,. Ideas of Human Actions often formed, he- 
fore the Actions tlLemselves exist. 

Let us suppose, in the first beginnings of society, 
a company of legislators met together, in order to con- 
sult on proper regulations for the government of the 
community. If they are- men of prudence and foresight,, 
they will naturally observe many new occurrences, 
likely to arise from this coalition of mankind, and 
their living together in crowds,*.- Perhaps the age in 
which they live, has not produced an instance of one 
man's killing another : yet from the knowledge of 
their own frame, and their power of doing hurt, they 
conceive this as a possible case, and are willing to pro- 
vide against it. Thus all the ideas that enter into the 
complex one of murder, are brought together, and 
united into one conception, before the action itself 
really exists. It is not, however, thought necessary to 
take into consideration the age of the person ; the 
chief thing in vievt^ being to prevent the putting an 
end to another's life unjustly, whether old or young; 
and therefore the penalty equally affects both cases. 
But when they come to consider the relation in which 
the person killed may stand to the murderer, here 
there appears a manifest difference; as it adds to the 
crime, when committed upon a benefactor, and ren- 
ders it particularly heinous in the case of a father. 
This last, therefore, is made to constitute a distinct spe- 
cies of action, and has a peculiar punishment allotted 
to it. Thus we see how men, according to their dif- 
ferent manner of life, and the relations they stand in 
to one another, are naturally led to form several col- 
lections of simple ideas, pre feredly to others, as fore-- 
seeing they may have frequent occasion to take notice 
of such precise combinations. And because it would 
be tedious in conversation, every time these complex 
notions occur, to enumerate all the ideas of which 
they consist; therefore, for the sake of ease and dis- 
patch, they give them particular names, and thereby 
render the compositions fixed and permanent. ^ 



Elements of logic. 45 

$£(?. xvn The necessity of Mutual Intercourse, and 

Men's particular Aims in Life, a great source cf Com- 
plex Ideas, 

That it is in this manner we eome by our complex 
ideas, which multiply upon us according as the exi- 
gencies ot' society require, or our pursuits, method of 
life, and different aims, throw occasions in our way> 
of combining such and such perceptions together, 
might be easily made to appear, by a short view of the 
combinations themselves. Human actions, as occur- 
ring most frecfuently, and affording large matter of 
conversation, debate, and inquiiy among men, have 
been very nicely modified, and distinguished into 
classes, according to the several circumstances most 
likely to attend them. In like manner, the arts and 
sciences, in proportion as they are cultivated, leading 
us into many compound views of things, which other- 
wise would never offer themselves to the considera- 
tion of the mind ; the complex ideas of this sort, 
with the names by which they are expressed, are, we 
iind, the work of such particular nations, >vhere thesfe 
arts and sciences have chieily flourished. The Greeks, 
for instance, excelled in learning and polite know- 
ledge ; hence many of the terms belonging to rhetoric, 
poetry, philosophy, physic, &;c. come originally from 
their language. Modern fortification has received its 
greatest improvements among the French ; and ac' 
cordingly the ideas and terms of the art are mostly deri- 
ved from writers of that nation. In Italy, architec- 
ture, music, and painting, have been the great exer- 
cise of the men of genius ; it is therefore among them 
that we find the several complex notions belonging to 
these parts of study, as well as the names by which 
they are expressed ; nor can we discourse accurately 
and minutely of the above-mentioned arts, without 
having recourse to the language of that climate. And 
i,f we descend into the particular callings and profes* 
■iions of men, they have all their peculiar collections of 
ideas, distinguished by their several names, and hardly 
known but to such as are conversant iu that r:;ann€r of 



46 ELEMENTS OF LOSIC. 

life. Thus calcination, cohobation, filtration, &c. ate 
words standing for complex ideas frequently framed in 
the minds of chjmists, and therefore familiar to men of 
that employment. Yet as these, and such like com- 
binations, seldom occur in common life, the generality 
of mankind, we see, are in a great measure unacquaint- 
ed with them. 

Sec. xvui,.,.HenC€ different sets of them prevail in dif- 
ferent Countries ; a7id Words in one Language have 

none to answer them in another, 

I might pursue these speculations farther, and show 
bow the several fashions, customs, and manners of oive 
nation, leading them to form many complex notions 
which come not so naturally in the way of another'; 
different sets of ideas prevail in different countries, 
and of course have names appropriated to them in 
the language, to which there are no words that an- 
swer in another. The procedure and forms of our 
courts of justice have introduced many terms into the 
English law, which stand for collections of ideas framed 
among no other people,.^Nor would it be possible to ren- 
der these terms by any single words of another lan- 
guage ; because, where ideas themselves prevail not, 
there are no names provided to express theni. In this 
case, therefore, it becomes necessary to use "circumlq- 
cutions, and enumerate the several ideas comprehended 
in the collectionj if ^,-e would so express ourselves, as 
to be understood in the language of other nations." 
Nay, even among the same people, the change of cus- 
toms and opinions frequently brings new sets of ideas, 
which, of course, must be distinguished by particular 
names ; while, at the same time, the notions of former 
ages grow into disuse, and the words answering them 
are wholly laid aside, or employed in a signification dif- 
ferent from what they had before. 

Sec, XIX,.,, This, too^ the cause that Languages are in a 
perpetual flux. 
Thus languages are in a perpetual flux, and by de- 
grees vaiy so much from their original frame, as to be- 
come unintelligible ev?n to the descendants of thos^ 



ELEMENTS OP LOOIC. 4? 

wlio speak them. If we run back into the ages of chi- 
valry in "England, when tilts and tournaments were in: 
fashion, how manj' complex ideas, peculiar to that mode 
of life, shall we find familiar among the men of those 
limes, which are now little known or attended to ? On 
the contrary, the improvements in arts and sciences 
that have since taken place, have led us into innumera- 
ble views of things, to which our fore-fathers were per- 
fect strangers. But I shall not push these reflections any 
farther, believing that what has been said will be suffi- 
cient to show the origin and progress of our compound 
ideas, and how the mind is directed in the choice of the 
combinations it makes. We therefore proceed to the 
consideration of abstract ideas, which make the subject 
of the following article. 



ART. II. 

OF ABSTRACT OR UNIVERSAL IDEAS* 

Sec. I..., .General Ideas formed by the Abstraction of 
the Mind. 
Having dispatched what was necessary to be said 
concerning our compound ideas, considered merely 
as they are combinations of the understanding, it is 
now time to explain how we come by our general no- 
tions, which serve to represent to us a multitude of in- 
dividuals and are the standards by v/hich we rank things 
into sorts. And this, as we have before intimated, is 
done by the abstraction of the mind ; which act may 
be extended to all our ideas, whether simple, compound, 
or of substances. If, far instance, we fix our attention 
on any particular colour, as scarlet, we can leave out 
the consideration of all present circumstances, as the 
subject in which it inheres, the time and place of seeing 
it, &c. and retaining only the impression itself, make 
it a representative of that quality or appearance, where - 
ever we chance to meet with it. It is thus that abstract 
and universal ideas are framed ; for the mind regarding 
only the scarlet colour, which one day it observes per- 



43 ELEMENTS 0¥ LOGIC. / 

haps in a piece of cloth, another in a picture, and 
a third in the rainbow ; the appearance is conceived to 
be the same in all these objects, and therefore is called 
by the same name. 

Sec. lu,.. .All the perceptions of the Understanding par- 
ticular. 
But to enter a little more closely into this matter, and 
show that these our general conceptions are the mere 
creatures of the understanding, it may not be amiss to 
take notice, that all our perceptions of things, whether 
we derive them from sensation or reflection, are of their 
own nature particular, and represent to us single, de- 
terminate objects. When we see a horse, for instance, 
in the fields, our idea is that of an individual. If we 
hear a sound, it is something particular, and different 
from what we hear at any other time. Every percep- 
tion of the mind is distincffrom every other perception ; 
nay, and every idea brought into view by the imagina- 
tion, as when we frame the image of a lion standing be- 
fore us, is still singular, and represents a single object. 

Seg. iii.....7%€ Idea of the Species represents what is 
common to different Individuals, 
But when we come to take a view of these several 
particulars, we readily observe among some of them 
a resemblance ; and framing to ourselves an idea of 
those things in which any of them are found to agree, 
we thereby get a general notion, applicable to many 
individuals. Thus horses are found to resemble one 
another in shape, voice, and structure of part^. The 
idea, which takes in only the particulars of this resem- 
blance, excluding what is peculiar to each single ani- 
mal, becomes of course common to all creatures of 
that kind, and is therefore the representative of a 
whole class of beings. Accordingly the name of that 
general idea is given to every animal in which that 
shape, voice, and structure is found; for the word 
liorse, implying 'only th^se particulars, must belong to 
all creatures wherein they exist. This is the first step 
or gradation in the forming of abstract notions, when 
the mind confines itself to the consideration of indivi- 



ELEMENTS OF LOGIC. ^49 

<iuals, and frames an idea that comprehends such only 
under it. The rank or class of things answering to 
this idea, is called species in the language of the 
schools. So a horse is a certain species of animals, an 
oak is a species of trees, and a square is a species of 
four-sided figures. 

Sec. IV The Idea of the Genus represents what is com- 
mon to several "Species, 
When we have thus learned to rank individuals into 
sorts and classes, according to the resemblance found 
among them, the mind proceeds next to consider the 
species themselves, and often in these too observes a 
certain likeness. Whereupon, throwing out all those 
particulars wherein the several species are found to 
disagree, and retaining only such as are common to 
them all, we thereby frame a still more general idea, 
comprehending under it a variety of different species. 
Thus a sparrow, a hawk, an eagle, &c. are distinct 
species of birds, which have each their peculiar shape 
-and make. They nevertheless resemble one another, 
in being covered with feathers, and provided with wings 
that be&r them through the air. Out of these parti - 
culars we form a new idea, including all the common 
properties of the feathered kind ; and appropriating to 
it the name o{ bird, mark by that word another class of 
things, of a higher order than any of the former. This 
superior division, which extends to several species at 
once, is called in the schools the ^e?ms, and is the second 
step the mind takes in advancing to universal notions. 

Sec. V The Mind may advance by manifold Grado 

ti&nSyin rising from Particulars to Generals. 
And thus have I given a short, but I hope intelligible 
account, of the business of genera and species, about 
which so much has been said in the writings of logi- 
cians. Species, in strictness and propriety of speech, is 
such a rank or class of things, as comprehends under 
it only individuals : genus advances still higher, and 
takes in a variety of distinct species. It is, haivever, to 
be observed, that the mind in rising from particulars to 
generals^ does not confine itself to one or two gra- 
E 



50 ELEMENTS OF LOGIC. 

dations, but may carry its views through the whole 
extent of things, until at length it arrive at an idea 
embracing the universal compass of nature. For when 
we have ranked things into sorts, and reduced these 
again to the higher order or genus, these genera are 
still found to resemble one another in some particu- 
lars, which being collected into one idea, form a new 
and more comprehensive division of things. Thus 
Inrd is a genus, embracing all the varieties of the fea- 
thered kind. Fish implies the several species of living 
creatures which inhabit the waters. Quadruped and 
insect are also universal ideas, that take in many infe- 
rior distributions and classes. Yet all these different 
orders of being, have this in common, that they are 
provided with organical bodies, fitted for the purposes 
of life and spontaneous motion. An idea, therefore, 
comprehending only these last particulars, will equally 
belong to all the divisions before enumerated ; and the 
word animal, by which it is expressed, becomes a gene- 
ral name for the several creatures endued with life, 
sense, and spontaneous motion. If we are for cany- 
ing our views still farther, and framing a yet more uni- 
versal notion, we can cast our eyes upon both the ani- 
mate and inanimate parts of nature ; wherein we find 
this mutual correspondence, that they exist, and con- 
tinue in being. This last' idea, therefore, of being in 
general, comprehends under it all the varieties of 
things, and may -be universally applied to whatever 
has either life or existence ; so that in re„spect of the 
present frame of nature, it is the highest and most uni- 
versal idea we have. 

Sec. vi...:.Whence many intermediate Steps between the 
highest Genus and lowest Species. 

In this series of notions, rising one above another, 
in the degree of universality, that division, which 
comprehends under it several genera, is called in the 
schools the higher genus ; which denomination con- 
tinues, \mtil we arrive at the last advance of the under- 
standing, when, being come to the most general of all 
ideas, that admits not of a superior, it is distinguished 



ELEMENTS OF LOGIC. 51 

by the name of the genus generalissimum. In like man- 
ner the several genera, comprehended under a higher 
g-enw5, are, in respect of it, considered as species; and 
as these two last have species under them, the inferior 
divisions are, for distinction's sake, termed lower spe- 
cies. Thus the progression continues, and when we 
come to the lowest subdivision of all, comprehending 
only individuals, which, as I have before intimated, 
constitutes the proper species^, this the schools denomi- 
nate the species specialissima. All that lie between 
it and the highest distribution of things, are the inter- 
mediate genera and species, w^hich are termed, each in 
their turn, genus generalius, or species specialiar, ac- 
cording as we consider them in the ascending or de- 
scending scale of our ideas ; or, to speak in the lan- 
guage 'of logicians, according to their ascent or descent 
w linea prcsdicameniali. I should not have entered so 
far into these verbal disquisitions, had not the terms 
here explained, been such as frequently occur in the 
writings of philosophers ; insomuch that without some 
knowledge of them we must often be at a loss, in the 
prosecution of these studies. Besides, it is both curious 
and useful, to see the gradual progress of the mind, in 
its advances from particular to general conceptions— 
to observe it ranging its ideas into classes, and esta- 
blishing a just and regular subordination in its views 
and notices of things. This is the shortest way to 
knowledge, and affords the best means of preserving the 
order and due connexion of our thoughts, so as to 
make them subservient to the increase of science. For 
when we see how things comprehend, or are compre- 
hended in, one another, we are able to discover the mu- 
tual dependence of all the several branches of know- 
ledge which leads us into the true and natural method of 
conducting our understandings in the search of truth. 

Sec. yu..,. General Ideas the Creatures of the Under- 
standing. 

From what has been said, it is evident, that general 
ideas are the creatures and inventions of the under- 
standing. Nature, it is true, in the production of 
things, makes, many of them alike : but it is the mind 



5:2 ELEMENTS OF LOGIC. 

alone, that collects the particulars in which they agrecj 
iatoone idea, and sets it up as a representative of many 
individuals. And now I think we may venture uponf 
that much-agitated question, where do Ihe genera and 
species of things exist ? To which I answer, in the 
mind. Universality belongs not to things themselves, it 
being apparent, that they are all particular in their ex- 
istence. However, as they often have many properties 
in common, the understanding, by uniting these inta 
one conception, obtains a general idea, under which it 
ranks all the several objects wherein these properties 
are found. So far indeed we must allow, that the par- 
ticular combination of properties, which constitutes the 
genus or species, exists in all the individuals referred to 
that genus or species ; but then it is in conjunction with 
other properties, by which these individuals are distin- 
guished from one other. Thus the collection of simple 
ideas, signified by the word bird, is to be found, for in- 
stance, in a hawk, or any other single animal, to which 
we apply that general name : but the notion itself, ab- 
stracted from all the particulars to which it belongs, 
has evidently no existence out of the understanding. 
There is not a being in nature that can be called a bird 
in genera], or that does not necessarily imply, in the 
very conception of it, several simple ideas, besides those 
marked by that word. For the name, in this case, sig- 
nifies no more than an animal covered with feathers, and 
provided with wings, without regard either to shape, 
bulk, or the particular time and place of its existence. 
These last considerations, however, are inseparable 
from the reality of things, and theref©re must be added 
4o the general idea, before we can conceive any thing 
conformable to it actually brought into being. 

^Ec. viu.... Considered apart, they exist only in the 
Mind, but in conjunction with other Ideas in the indi- 
viduals comprehended utider them. 

Hence we see at once, what sort of an existence ge- 
neral natures have. Considered apart, and by them- 
selves, they are wholly the workmanship of the under- 
standing, and derive their being and reality from it ; 
but viewed in conjunction with other ideas that co-exi.^t 



ELEMENTS OF LOGIC. 53 

with them in the several objects of nature, they are to 
be found in the individuals to which they refer ; and 
therefore, according to this way of conception, may be 
said to have an existence in them. Thus, so long as 
the ideas answering to the words man or tree, continue 
general and undetermined, they have no real objects 
answering them in nature ; nor can the collections of 
simple ideas, marked by these names, while all others 
are supposed excluded, exist an3^ where out of the un- 
derstanding. Nevertheless, as all the simple ideas, in- 
cluded in the general notion ot man, are to be found in 
every particular ?7iG?i — and all those implied in the no- 
tion t)f a tree, in every particular tree — hence the general 
nature of 7naw, exists in every individual mati, as does 
the general nature of a tree, in every individual tree. 
Sec. IX.... Difference of Ideas considered as compound 
and as universal. 
One thing still remains to be observed, with regard 
to these our general ideas ; that, though many of them 
are evidently combinations of different simple ideas, and 
according to that way of considering them, are includ- 
ed in the first division of our complex conceptions, those , 
namely, framed by the composition of the mind ; yet 
we are carefully to distinguish between an idea, as it is 
compound, and as it is universal. In the first case, the 
mind chiefly considers the several ideas that are com- 
bined together ; or, in other words, all the attributes, 
qualities, or parts, that are contained in any idea. Thus 
the idea of a bird, includes life, sense, spontaneous mo- 
tion, a covering of feathers, wings, &c. none of which 
can be left out without destroying the very nature of 
the idea, and making it something quite different from 
what it was before. This way of considering things 
according to the number of their parts and properties, 
is called by logicians the comprehension of an idea. But 
the universality of our notions implies quite another 
turn of thinking, inasmuch as it fixes the regard of 
the mind upon the subject to which our ideas extend, or 
the individuals and species comprehended under them. 
In this sense, the idea answering to the word bird, takes 
in the several species of the feathered creationjtbe hawk^ 
E 2 



54- ELEMEA'TS OF LOGIC, 

the eagle, sj^arrow, lark, and innumeraule olliers, to .'ill 
which it may with equal propriety be applied. And 
here it is remarkable, that the idea loses nothing of its 
force or conrprehension , by being restricted to a parti- 
cular kind. When I say the bird of Jove, though in 
this case the idea is restrained to the eagle alone, it still 
remains as distinct, and includes as many simple ideas 
in' its composition, as when, before, it was extended to 
all the different tribes of feathered animals. 
Sec. .x....77ie comprehension and extensioij, of our Ideas, 
We see, therefore, that our compound ideas may 
continue the same in respect of their attributes, or the 
number of parts, and yet vary considerably in the degree 
of universality. The general idea of 7ncf?i is the same, 
whether applied to the whole human race, or those of 
any particular nation. When I affirm, for instance, of 
mankind in general, that their knowledge falls short of 
perfection, and afterwards make the like observation of 
the men of the present age ; in both cases, the word 
man stands for one and the same collection of simple 
ideas; but in respect of the individuals to which it is 
■applied, there is a great and manifest difference. That 
is the term, man, denotes one invariable compound 
idea ; which, notwithstanding^, considered as a general 
notion, may be contracted or enlarged at pleasure. 
And as in the former case, the several parts of the com- 
pound idea are called its comprehension ; so in the lat- 
ter, the individuals, to which the universal idea ig ap- 
plied, are called its extension. 1 might add many more 
observations on this subject, but choose rather to stop 
here, having said enough to explain the difference be- 
tween compound and abstract ideas, and show the rea- 
son of ray ranging them under distinct heads. 

ART. III. 

OF OUR IDEAS OF RELATIONS. 

SeC> 1.... Ideas of relations exceeding numerous. 
I COME now to the third and last division of those 
ideas,, which I consider as the creatures and work- 



ELEMENTS OF LOiiiC* t)^ 

manship of tlwi iinderstandir)^ ; such, nomely, as arl?> 
from the comparing of things one with another. For 
the mind in its views is not tied to single objects ; but 
can examine their references and respect?, in regard to 
others, brought under consideration at the same time. 
And when it does so, and thence derives new notice of 
things, the ideas thus got are called relations, and make, 
I am apt to think, the largest class of all our percep- 
tions. For every single object will admit of almost in- 
numerable comparisons with others, and in this sense 
may become a ver}^ plentiful source of idea? to the un- 
derstanding. Thus if we compare one thing with ano- 
ther, in respect oi bulk, we get the ideas oi greater, less^ 
or equality ; if in respect of time, of older and younger ; 
and so for other relations, which we can pursue at plea- 
sure, almost without end ; whence it is easy to conceive, 
Low veiy extensive this tribe of our perceptions must be. 

Sec. II. ...Men chiejly determined to particular Com- 
parisons by the Wants and Exigencies of Life. 

I shall not pretend to trace out these ideas particu- 
larly, nor indeed so much as to enumerate their several 
divisions; it being enough to observe, that here, as 
well as in the other kinds of our complex ideas, we 
bound ourselves, for the most part, to such comparisons, 
as the exigencies of society, the wants of life, and the 
different professions of men, render necessar}'- ; and are 
more or less accurate in tracing out the relations of 
things, according to' tl^ degree of importance they 
appear to have in these respects. The relations of 
men one to another, arising either from the ties of blood, 
their several ranks and places in the community, or a 
mutual intercourse of good offices, being of great weight 
and concern in the commerce of life, have in a particu- 
lar manner engaged our attentioii, and are therefore 
very minutely described. For the same reason, men 
have found it necessary, to determine, as exactly as 
possible, the various dependence of things, as their 
happiness is nearly connected with this knowledge. 
When we consider objects merely in respect of exist- 
ence, as either giving or receiving it, we come by the 
ideas of cause and effect : nor need I mention how much 



56 ELEMEx^TS OF LOGIC. 

the welfare of mankind depends on an extensive view 
of things, as they stand connected in this relation ; it 
being evident, that the several schemes and purposes of 
life are all conducted upon a previous supposition, that 
certain known causes will have their usual regular ef- 
fects, and such and such actions be attended with such 
and such consequences. 

Sec. 111.... Relations of Creator and Creature, S,x. 
But there are other relations of this kind, besides 
those that regard merely existence ; as when we also 
take into the account the additional gifts of a capa- 
city for happiness, and the means of attaining it ; 
which constitutes the relation oi Creator and creature^ 
in the more solemn acceptation of these words. Again, 
when we consider the great Author of our being, not 
only as the Creator of the universe, but also as pre- 
serving and holding it together, and presiding over the 
present frame of things w^ith uncontrouled dominion ; 
he then appears under the notion of a moral Governor ^ 
to whom we are accountable for our actions, and the 
use we make of those powers and faculties we derive 
from him. Now as it is of the highest consequence 
for men, not to be unacquainted with these, and such 
like relations ; hence we lind, that the wisest nations, 
and such as best understood the true application of the 
powers of the mind, have always made it their chief 
study to regulate and ascertain these ideas, and trace 
them in all their consequences. And thus we may, in 
some measure, perceive, how the mind proceeds in 
comparing its ideas together, and by what views it is 
chiefly governed, in framing the complex notions of this 
class, by which it represents the various habitudes of 
things, I shall only add upon this subject, these two 
observations. 

SjEc. IV.... Ow?* Ideas of relations very clear and distinct. 
First, that our ideas of relations, are for the most 
part very clear and distinct. For the comparing of 
things together, being a voluntary act of the mind, 
we cannot but suppose that it must be acquainted with 
its own views in the comparison ; and of course have 
a clear conception of the foundation of that relation. 



ELEMENTS OF LOGIC. ^7 

it sets itself to inquire into. Thus the relation of 
cause and etTect, implying only that one thing- produ- 
ces, or is produced by another, which notions are al- 
ways distinctly settled in the understanding before it 
goes about to make the comparison ; it is evident, 
that the idea representing this mutual respect of ob- 
jects, will be no less clear, than are the notions them- 
selves upon which the relation is founded. And what 
is still more remarkable of the ideas of this class ; 
they cease not to be distinct, even where the subjects 
compared are but very imperfectly known. For I can 
well enough conceive, that one thing has produced 
another, and that therefore they stand related as cause 
and effect, though my ideas of the things themselves 
may perhaps be very obscure, and come far short of 
representing their real nature and properties. I doubt 
not but it will be readily own^d, that our idea of the 
universe, considered as comprehending the whole 
frame of created things, is very inadequate ; and I 
think it is still more apparent, that our notion of the 
Supreme Being comes not up to the excellence and 
perfection of his nature. Yet we very well understand 
what is meant by calling God the Author of the 
world ; and though we comprehend not the manner 
of his producing it, find no difficulty in framing the 
ideas, the relative words Creator and creature stand for. 

Sec. V Ideas of Relations among the most important 

Conceptions of the Mind. 

I have yet another observation to make upon this 
subject ; and it is, that our ideas of relations are among 
the most important conceptions of the understanding, 
and afford the largest field for the exercise and im- 
provement of human knowledge. Most of our in- 
quiries regard relative ideas, and are set on foot with 
a view to investigate the mutual habitudes of things. 
The mathematician has taken quantity for his province, 
and teaches us how to compare magnitudes of differ- 
ent figures and dimensions, in order to judge with 
certainty of their relative properties. The philosopher 
attaches himself to tlte cbain-of causes and effects, and 



58 ELEMENTS OF LOGIC. 

endeavours to trace out the various dependence of 
things considered in this light. In fine, whither do 
all our researches tend, but by means* of certain 
known properties and relations, to find out others" that 
stand some how connected with them ? As for the 
importance of these conceptions, no one can call that 
in question, who reflects ; that from our relations to 
our Creator and one another, arise all the duties of 
morality and religion, and that the correspondence of 
the several objects of nature, to the organs of the 
body, and faculties of the mind, is that by which 
alone we can judge of what will procure us happiness 
or misery. Whence it is evident, that w^ithout an 
exact knowledge of these relations, we must wander 
on in life with great uncertainty, and may often plunge 
into calamities and misfortunes, by those very pur- 
suits from which we expected nothing but joy and 
pleasure. 

Sec. VI,... Recapitulation, 

Thus have I gone through the several divisions^ 
our ideas, which I have endeavoured to represent in 
such a manner as their vast extent may most easily ap* 
pear, and the conduct of the mind in framing them 
be distinctly apprehended. I might easily run into 
other distinctions, by considering them as clear or 
obscure, adequate, or inadequate, true or false. But 
the limits of this tract will not allow my entering 
more fully into the subject, and I think it the less 
needful, because the very names are almost sufficient 
to convey a notion of these several kinds of ideas into 
tiie mind. But as the division explained above seems 
to be of great importance, towards settling in the un- 
derstanding a just'view of the progress of human know- 
ledge, and the steps by which it advances from one 
degree of improvement to another, I shall here run 
over it again in as few words as possible, that the 
whole process may be seen at once. Our ideas are all 
derived into the understanding, either by sensation or 
reflexion. This, however, is observable, that one and 
the same object often excites a variety of perceptions. 



ELEMENTS OF LOGIC. 59 

at once, which are nevertheless readily distinguish- 
ed by the mind, and appear each under a form pe- 
culiar to itself. These constitute our primary and" 
original notices, and are easily known from all others 
inasmuch as they are entirely void of plurality, and 
cannot be divided into two or more different ideas. 
They are also the materials out of v/hich the others 
are formed, and are therefore, by way of distinction, 
cjilled simple ideas. But the mind, though it has no 
power over these, either to fashion or destroy them, 
can yet combine them in an infinite number of ways ; 
and from their various combinations result all our 
complex ideas, which are of two principal kinds. First, 
such as are derived from without, and represent those 
combinations of simple ideas, that have a real existence 
in nature. Of this sort are all our ideas of substance. 
Secondly, the conceptions formed by the mind itself, 
arbitrarily uniting and putting together its ideas. And 
as this makes by far the largest class, and comprehends 
all those ideas which may be properly termed our own, 
as being the real workmanship of the understanding ; so 
they fall very naturally under three distinct heads. For 
either the mind combines several simple ideas together, 
in order to form them into one conception, in which 
the number and quality of the ideas united, are prin- 
cipally considered ; and thus it is we come by all our 
compound notions : or it fixes upon any of its ideas, 
whether simple, compound, or of substances ; and leav- 
ing out the circumstances of time, place, real exist- 
ence, and whatever renders it particular, considers the 
appearance alone ; and makes that a representative of 
all of the kind ; whence our abstract and universal 
ideas are derived : or lastly, it compares things one 
with another, examines their mutual connexions, and 
thereby furnishes itself with a new set of notions, 
known by the name of relations, which, as has been al- 
ready remarked, make by ho means the least important 
class of our perceptions. This division of our ideas, 
as it seems to be the most natural, and truly to repre- 
sent the manner in which they are introduced into the 
mind, so I believe it will be found to comprehend them 



60 eleme?;ts of logic. 

in all their varieties. I shall therefore now proceed to 
efFersome observations upon language, as being the 
great instrument, by which we are enabled to make our 
ideas and perceptions known toothers. 



CHAP. V. 

OF WORDS, CONSIDERED AS THE SIGNS OF OUR IDEAS. 



Sec. J. ...Words furnish the means of recording our 
own Thoughts. 

We have seen how the mind comes to he first 
furnished with ideas, and by what methods it con- 
trives to diversify and enlarge its stock : let us now 
consider the means of making known our thoughts to 
•others, that we may not only understand how know- 
ledge is acquired, but also in what manner it may be 
communicated with the greatest certainty and advan- 
tage. For our ideas, though manifold and various, ar^ 
nevertheless, all within our own breasts, invisible to 
others, nor qan of themselves be made to appear. But 
God designing us for society, and to have a fellowship 
v>'ilh those of our kind, has provided us with organs fit- 
ted to frame articulate sounds, and given us also a ca- 
pacity of using those sounds as signs of internal con- 
ceptions. Hence spring words and languages ; for 
(having once pitched upon any sounr^, to stand as the 
mark of an idea in the mind, custom, by degrees, estab- 
lishes such a connexion between them, that the appear- 
ance of the idea in the understanding always brings 
to our remembrance the sound or name by which it is 
expressed ; as, in like manner, the hearing of the sound 
never fails to excite the idea for which it is made to 
stand. And thus it is easy to conceive, how a man 
may record his own thoughts, and bring them again 
into view, in any succeeding period of life. For this 
connexion being once settled, as the same sounds will 
always serve to excite the same ideas ; if he can but 



ELEMENTS OF LOGIC. bl 

GOiitrive to register his words, in the order and dispo- 
sition in which the present train of his thoughts pre- 
&€nts them to his imagination ; it is evident he will be 
able to recall these thoughts at pleasure, and that too 
in the very manner of their first appearance. Accord- 
ingly we find, that the inventions of writing and paint- 
ing, by enabling 4js to fix and perpetuate such perish- 
able things as sounds, have also furnished us v/ith the 
means of giving a kind of permanency to the transac- 
tions of the mind, insomuch that they may be in the 
same manner subjected to our review, as any of the other 
abiding objects of nature. 

Sec. u....And of the mutual Communication of Know- 
ledge from one Man to another. 

But besides the ability of recording our own thoughts 
there is^ this farther advantage in the use of external 
signs, that they enable us to communicate our senti- 
ments to others, and also receive information of what 
passes in their breasts. For any number of men, hav- 
ing agreed to establish the same sounds as signs of the 
same ideas, it is apparent, that the repetition of these 
sounds must excite the like perceptions in each, and 
create a perfect correspondence of thoughts. AVhen, 
for instance, any train of ideas succeed one another in 
my mind, if the names, by which I ahi wont to express 
them, have been annexed by those with whom I con- 
verse, to the very same set of ideas, nothing is more 
evident, than that by repeating those names, according 
to the tenor of my present conceptiona, I shall raise in 
their minds the same course of thought as has taken 
possession of my own. Hence, by barely attending to 
what passes within themselves, they will also become 
acquainted with the ideas in my own understanding, 
and have them in a manner laid before their view. 
So that we here clearly perceive, how a man may com- 
eiunicatehis sentiments, knowledge, and discoveries 
to others, if the language in which he converses, be 
extensive enough to mark all the ideas and transactions 
of his mind. Bui as this is not always the case, and 
iKien are often obliged to invent terras pf their own, to 
F 



62 ELEMENTS OP LOGIC, 

express new views and conceptions of things ; it may Ue 
asked, how, in these circumstances, we can become ac- 
quainted with the thoughts of another, when he makes 
use of words to which we have never annexed any ideas, 
and which, of course, can raise no perceptions in our 
minds ? Now, in order to unveil this mystery, and give 
some little insight into the foundation, growth, and 
improvement of language, the following observations 
will, I am apt to think, be found of considerable moment. 

Sec. III. ...Simple Ideas cannot be conveyed into the Mind 
by Words, or a Description ; 

First, that no word can be to any man the sign of an 
idea, till that idea comes to have a real existence in his 
mind. For names being only so far intelligible, as 
they denote known internal conceptions, where they 
have none such to answer them, there they are plainly 
sounds without signification, and of course convey no 
instruction or knowledge. But no sooner are the ideas 
to which they belong raised in the undetstanding, than, 
finding it easy to connect them with the established 
names, we can join in any agreement of this kind made 
by others, and thereby enjoy the benefit made by their 
discoveries. The first thing, therefore, to be consider- 
ed, is, how these ideas may be conveyed into the mind ; 
that, being there, we may learn to connect them with 
their appropriated sounds, and so become capable of 
understanding others, when they make use of these 
sounds in laying open and communicating their thoughts. 
Now to comprehend this distinctly, it will be necessa- 
ry to call to mind the before-mentioned division of 
Gur ideas into simple and complex. And first, as for 
our simple ideas, it has been already observed, that 
they can find no admission into the mind, but by tWo 
original fountains of knowledge, sensation and reflex- 
ion. If therefore any of these have as yet no being 
in the understanding, it is impossible by words, or a 
description, to excite them there. A man, who had 
never felt the impression of heat, could not be brought 
to comprehend that sensation J by any thing we might 
say to explain it. If we would really produce the idea 



ELEMENTS OF LOGIC. 63 

in him, it must be by applying the proper object to his 
senses, and bringing him within the influence of a hot 
body. When this is done, and experience has taught 
him the perceptions to which men have annexed the 
name, heat, it then becomes to him the sign of that 
idea ; and he thenceforth understands the meaning of 
a term, which, before, all the words in the world would 
not have been sufficient to convey into his mind. The 
case is the same in respect of light and colours. A man 
born blind, and thereby deprived of the only convey- 
ance for the ideas of this class, can never be brought 
to understand the names by which they are expressed. 
The reason is plain : they stand for ideas that have no 
existence in his mind ; and as the organ appropriated to 
their reception is wanting, all other contrivances are 
vain, nor can they, by any force of description, be rais- 
ed in his imagination. But it is quite otherwise in our 
complex notions. For these being no more than cer- 
tain combinations of simple ideas put together in va- 
rious forms — if the original ideas, out of which these 
collections are made, have already got admission into 
the understanding, and the names serving to express 
them are known — it will be easy, by enumerating the 
several ideas concerned in the composition, and mak- 
ing the order and manner in which they are united, 
to raise any complex conception in the mind. Thus 
the idea answering to the word rainbow^ may be readi- 
ly excited in the imagination of another, who has ne- 
ver seen the appearance itself by barely describing the 
figure, largeness, position, and order of colours ; if we 
suppose these several simple ideas, with their names, 
sufficiently known to him. 

Sec. IV. ...The .Nature of Complex Ideas Definable^ those 
of Simple Ideas not. 

And this naturally leads me to a second observation 
upon this subject, namely, that words standing for 
complex ideas are all definable ; but those, by which 
we denote simple ideas, are not. For the perceptions 
of this latter class, having no other entrance into the 
mind, than by sen&ation or reflexion, can onh' bo ur- 



^'4 ELEMENTS OF LOGIC, 

quired by experience from the several objects of nature., 
proper to produce those perceptions in us. Words, 
indeed, may very well serve to remind us of them, if 
they have already found admission into the understand- 
ing, and their connexion with the established names is 
known ; but they can never j^ive them their original 
being and existence there. And hence it is, that when 
any one asks the meaning of a word denoting a simple 
idea, we pretend not to explain it to him by a defini- 
tion, well knowing that to be impossible; but suppos- 
ing him already acquainted with the idea, and only 
ignorant of the name by which it is called, we either 
mention it to him by some other name, with which we 
presume he knows its connexion, or appeal to the ob- 
ject where the idea itself is found. Thus, was any one 
to ask the meaning of the word white, we &hoii\die\\ 
him it stood for the idea, as albus, in Latin, or blanc, in 
French : or, if we thought him a stranger to these lan- 
guages, might appeal to an object producing the idea, 
by saying, it denoted the colour we observe in snow or 
milk. But this is by no means a definition of the word, 
exciting a new idea in his understanding ; but merely a 
contrivance to remind him of a known idea, and teach 
him its connexion with the established name. For if 
the idea after which he inquires, has never yet been 
raised in his mind — as suppose one, who had seen no 
other colours than black and white, should ask the mean- 
ing of the word 5car/e^ — it is easy to perceive, that it 
v/ould be nomore possible tomake him comprehend it by 
words, or a definition, than to inculcate the same per- 
ception into the imagination of a man born blind. 
The only method in this case, is, to present some ob- 
ject, by looking at which the perception itself may be 
excited ; and thus he will learn both the name and the 
idea together. 

Sec. v. ...Experience and Observation bring Men to o/n 
Agreement in the Names of Simple Ideas. 

Should anyone's curiosity now prompt him to inquire, 
how it comes to pass, that men agree in their names ot 
he simple idea?, seeing they cannot viev/ the percep- 



lllLEMEiVTS OF LOGIC. 65 

lions in one another's minds, nor make known these 
perceptions by words to others ; I answer, that the ef- 
fect here mentioned is produced by experience and ob- 
Fcrvation. Thus, finding, for instance, that the name, 
heat, is annexed to that impression w^hich men feel 
when they approach the fire, I make it also the sign of 
the idea excited in me by such an approach, nor have 
any doubt, but it denotes the same perception in my 
mind as in their's. For we are naturally led to ima- 
gine, that the same objects operate alike upon the or- 
gans of the human body, and produce an uniformity of 
sensations. No man fancies, that the ideas raised in 
him by the taste oi sugar, and wdiich he c^lhsweeA- 
ness, differs from that excited in another bj^ the like 
means, or that wormwood, to whose relish he has given 
the epithet ^i7<er, produces in others the sensation which 
he denotes by the word sweet. Presuming, therefore, 
upon this conformity of perceptions, when they arise 
from the same objects, we easily agree as to the names 
of our simple ideas ; and if at ?..ny time, by a more 
narrow scrutiny into things, new ideas of this class 
come in our way, which we choose to express by terms 
of our own invention ; . these names are explained not by 
a definition, but by referring to the objects, whence the 
ideas themselves may be obtained. , 

Sec. vi....77ie Conveyance of Complex Ideas by Dejini- 
tions, a wise Contrivance in JVature ; 

Being in this manner furnished with simple ideas, 
and the names by which they are expressed, the meaning 
of terms that stand for complex ideas is easily attain- 
ed ; because the ideas themselves answering to these 
terms, may be conveyed into the mind by definitions. 
For our complex notions, as was already observed, are 
only certain combinations of simple ideas. When, 
therefore, these are enumerated, and the manner in 
which the}'' are united into one conception explained, 
nothing more is wanting to raise that conception in the 
understanding ; and thus the term denoting it comes 
of course to be understood. And here it is worth while 
to reflect a little upon the wise contrivance of nature. 
F 2 



Q^ ELEMENTS OF LOGIC 

in thus furnishing us with the very aptest means of 
communicating our thoughts. For were it not so or- 
dered, that we could thus convey our complex ideas 
fiom one to another by definitions, it would in many 
cases be impossible to make them known at all. This 
is apparent in those ideas which are the proper work 
of the mind. For as they exist only in the understand- 
ing, and have no real objects in nature, in conformity 
to which they are framed, — if we could not make them 
known by a description, they must lie forever hiddeo 
within our own breasts, and be confined to the narrow 
acquaintance of a single mind. All the fine scenes, that 
rise from time to lime in the poet's fancy, and, by his 
lively painting, give such entertainment to his readers . 
— were he destitute of this faculty, of laying them 
open to the view of others by words and descriptions, 
— could not extend their influence beyond his own 
imagination, or give joy to any but the original in- 
ventor. 

Sec. YU...,And of great avail towards the Lnprcvement 
of Knowledge. 

There is this farther advantage in the ability w-e en- 
joy, of communicating our complex notions^ by defini- 
tions ; that as these make by far the largest class of our 
ideas, and most frequently occur in the progress and 
improvement of knowledge ; so they are by this means 
imparted with the greatest readiness, than which no- 
thing could tend more to the increase and spreading of 
science. For a definity is soon perused, and if the 
terms of it are well understood, the idea itself finds an 
easy admission into the mind. Whereas in simple 
perceptions, where we are referred to the objects pro- 
ducing them, if these cannot be come at, as is some- 
times the case, the names by which they are expressed 
must remain empty sounds. But new ideas of this 
class occurring very^ rarely in the sciences, they sel- 
dom create any great obstruction. It is otherwise with 
our complex notions ; for every step we take, leading 
us into new combinations and views of things, it be- 
comes necessary to explain these to others, before they 



EJ.EMEXTS OF LOGIC. 6/ 

caii be made acquainted nith our discoveries. And as 
the manner of definitions is easy, requiring no appara- 
tus but that of words, which are always ready, and at 
hand ; hence we can, with the less difficulty, remove 
such obstacles, as might arise from terms of our own 
invention, when they are made to stand for new com- 
plex ideas, suggested to the mind by seme present train 
of thinking. And thus at last we are let into the mys- 
tery hinted at in the beginning of this chapter, x?>. 
how we may become acquainted with the thoughts of 
another, when he makes use of words to which we have 
as j^et joined no ideas. The answer is obvious, from 
what has been already said. If the ternis denote simple 
perceptions, he must refer us to those objects of nature, 
whence the perceptions themselves are to be obtained ; 
but if they stand for complex ideas, their meaning may 
be explained by a definition. As for the names of sim- 
ple ideas, 1 shall here dismiss them ; it being sufficient 
to take notice, that our knowledge this way can be ex- 
tended only by experience and observation. But thiS 
theory of definitions making a material part of logic, 
and being indeed of great importance towards the im.- 
provemient of human knowledge, it will be necessary 
to lay it a little m.ore open to the view of the reader. 

Sec. VIII. ...T/te Composition and Resolution of cur 
Complex Ideas. 

Complex ideas are, as has been already said, no other 
than simple ideas put together in various forms. Bui 
then it is to observed, that in making these collec- 
tions, the mind is not always tied down to the im.medi- 
ate view of the simple perceptions out of which they are 
framed. For if we suppose the understanding already 
furnished with a considerable stock of compound no- 
tions, these again may be made the constituent parts of 
others still more compounded, insomuch that the new 
idea thence arising may be termed a combination of 
complex conceptions. Thus the idea annexed to the 
word animal, includes many perceptions under it, as 
life, sense, spontaneous motion, &:c. In the like man- 
ner by tlie term rational, we denote a variety of simple 



C8 ELEMENTS OF LOGIC. 

ideas. If now combining these two conceptions togc 
ther, we form the still more complex notion of a ration- 
al animal ; the idea thus got is truly a collection of 
compound notices. In a word, the same thing- happens 
here as in numbers, which we may consider not onl}' 
as various collections of units, these being indeed their 
original and constituent parts ; but also as sometimes 
composed of other lesser numbers, which, all put toge- 
ther, make up the respective sums. Now in tracing 
any very large number, when, for the ease of the mind- 
, we consider it at first as composed of various others still 
less — if we next take these less -parts to pieces, and 
pursue them continually, until we arrive at the units 
out of which they are composed ; we thereby totally 
unravel the collection, and being able to push our re- 
searches no farther, rest satisfied in the view thus offered 
to the understanding. Jiist so it is in the examination 
of our complex ideas. For when any very compounded 
notion comes under the inspection of the mind, in or- 
der to be traced to its first principle — we begin with 
resolving it into other idfeas less complicated ; and taking 
these again to pieces, one by one, still go on with the 
search, until we have broken the whole into our first 
and simple perceptions, beyond which the pursuit can- 
not possibly be carried. And this is the reason why I 
have all along called' our simple ideas tlie foundation 
and groundwork of human knowledge ; because, in 
unravelling the conceptions of the mind, we find our- 
selves at length bounded by these ideas, which are in- . 
deed the last resort of the understanding. 

Sec. IX. ...The Karnes of Simple Ideas may he consider- 
ed as the Elementary Paris of Language, 

From what has been said, it will be easy to cpnceive^ 
how, in defining a tenn, standing for any very complex 
idea, other terms may be introduced, that also denote 
compound ideas, though of an inferior class. For the 
first idea being resolvable into others less complicated ; 
the definition, which enumerates these component ideas, 
must consist of the names by which they are expressed. 
And if it so happen, that the ideas of this second class 



ELEMENTS OF LOGIC. 69 

?pe also unknown, their terms, too, oug-ht to be still (at-' 
ther defined. In this manner may a series of definitions 
be carried on, until we arrive at the names of simple 
ideas, which not being definable, the analysis must ne- 
cessarily cease. And thus we see, that as our simple 
ideas are the materials and foundation of knowledge, so, 
the names of simple ideas may be considered as the ele- 
mentary parts of language, be3^ond which we cannot 
trace the meaning and signification of words. When 
we come to them, we suppose the ideas they stand for 
already known ; or, if they are not, experience alone 
ii-ust be consulted, and not definitions or explications. 
And here it is well worth our notice, that as the names 
cf these our original conceptions, constitute the primi- 
tive and fundamental articles of speech, upon which 
the whole superstructure of human language is built, 
so ihey are, of all others, the least doubtful and uncer- 
tain in their signification. Because, standing each for-' 
one simple perception, not precariously excited in the 
mind, but^ the effect of certain powers in things, fitted 
to produce that sensation in us ; there is no danger of 
error or mistake. He that once knows sweetness to be 
the name of the taste received from sugar, -whiteness 
of the colour in snow or milk, and heat of the sensation 
produced by approaching the fire, will not be apt to 
misappl}^ those words, or annex them to perceptions of 
a different kind. And as the names of complex ideas 
may all be resolved into these primitive terms, it is ap- 
parent, that we are sufficiently provided with the means 
of com.municating our thoughts one to anothri ; and 
that the mistakes so frequently complained of on this 
head, are wholly owing to ourselves, in not Hhnciently 
defijiing the terms v.e use, or perhaps net connecting 
th^m with clear and determinate i^eas. 



EtEMENTS 0F LOGIC; 



'CHAP. VI. 

OF DEFINITION, AND ITS SEVERAL KI^SfDS, 

Sec. I. ...The Variety of Definitions proceeds from the 
various Applications of Words. 
Having laid these foundations, shown what words 
are, and what are not definable, and taught the 
manner of resolving our notions, as well as lan- 
guage itself, into its first and original principle ; we 
now proceed to explain a little more particularly the 
nature of definition, and the several kinds made use 
of, according to the different views men have in com- 
municating their thoughts one to another. Definitions 
^ are intended to make known the meaning of words 
standing for complex ideas ; and were we always care- 
ful to form those ideas exactly in our minds, and copy 
our definitions from that appearance ; much <ef the con- 
fusion and obscurity complained of in languages might 
be prevented. But, unhappily for us, we are by no 
means steady in the application of names, referring 
them sometimes to one thing, sometimes to another; 
which often creates great uncertainty in their signifi- 
cation, and obliges us to give a different turn to our de- 
finitions, according to the different reference of the 
terms defined. In order, therefore, to render this 
whole matter as clear and obvious as possible, we shall 
first consider to what it is that names, in the use of 
language, are most commonly applied ; and then from 
the variet}'" of this application, endeavour to account 
for the several methods of defining, mentioned in the 
writings of logicians. 

Sec. u... .Words have a threefold Reference; to our 
own Ideas, those of others, and the real being of things. 
Words then have manifestly a threefold reference. 
First, and more immediately, they denote the ideas in 
the mind of him who uses them ; and this is their true 
and proper signification. When a man speaks, it is 



ELEMENTS 0¥ LOGIC. 7! 

that he may be understood ; and the words he em- 
ploys to convey his thoughts, are such as by use he has 
learned to connect with the ideas then present to his 
mind. But because those with whom we converse, are 
also supposed to know the meaning of the terms we 
use, hence, secondly, we consider our words as signs, 
likewise, of the ideas in their minds; and this is the 
foundation of what is called propriety in language, 
when men take care to affix such notions to their words, 
as are commonly ^applied to them by those of most un- 
derstanding in the country where they live. The third 
and last reference of words is to things themselves. 
For many of our ideas are taken from the several ob- 
jects of nature, wherewith we are surrounded ; and 
being considered as copies of things really existing, 
the words , by which they are expressed, are often trans- 
ferred from the ideas themselves, to signify those ob- 
jects which they are supposed to represent. Thus the 
word, sun, not only denotes the idea excited in the 
mind by that sound, but is also frequently made to 
stand for the luminous body itself, which inhabits the 
centre of this our planetary system. Now, according 
this threefold application of names, their definitions, 
and the manner of explaining them, must be various; 
for it is one thing to unfold the ideas in a man's 
own mind, another to describe them, as they are sup- 
posed to make their appearance in the minds of others ; 
and lastly, it is something still different, to draw 
images or pictures, that shall carry in them a conform- 
ity to the being and reality of things. But we shall 
treat of e,ach in order. 

Sec. ui..,.Definitionsof ike Name teach cnly the Con- 
nexion of our Words and Ideas, and are therefore 
arbitrary. 

First, then, when we consider words, as signs of the 
ideas in the mind of him who uses them ; a definition 
\s nothing else, but such an explication of the meaning 
of any term, as that the complex idea annexed to it by 
the speaker, may be excited in the understanding of 
him with whom he converses. And this is plainly no 



72 ELEMENTS OF LOGIC. 

more than teaching the connexion of our words and 
ideas, that others may understand the sense of our ex- 
pressions, and know distinctly what notions we affix to 
the terms we use. When we say, for instance, that 
by the word square we mean a figure bounded by four 
equal sides, joined together at right angles; what is 
this but a declaration, that the idea of a quadrilateral, 
equilateral, rectangular figure, is that which in dis- 
course or writing we connect with the term square ? 
This is that kind of definition, which logicians call 
the definition of the name ; because it discovers the 
meaning of the words or names we make use of, by 
showing the ideas for which they stand. Now, as sounds 
are of themselves imiifferent to signify any ideas, 
hence it is plain, that the definitions of names are arbi- 
trary, every man having a liberty to affix what notions 
he pleases to his words. But the convenience of com- 
munication making it necessary for men speaking tlie 
same language to agree as nearly as possible in the sig- 
Dification of sounds, a conformity has accordingly been 
studied. Nevertheless, we find that differences will 
i-fHntime to time creep in, which must create great 
confusion in men's discourses and reasonings, if they 
are not careful to define their terms, that their signifi- 
cation may be kept fixed and steady, and lie always 
open to the view of the mind. The writings of the 
mathematicians are a clear proof, how much the ad- 
vancement of human knowledge depends upon a right 
use of definitions. For as by means of them they 
every where preserve ^;he same determined significa- 
tion to their words, hence there is little dispute as to 
the meaning"^ of their expressions, almost all men un- 
derstanding them in the same sense. And thus it hap- 
pens, that such as apply their thoughts this way, hav- 
ing perfectly the same views of things, readily compre- 
bend the discoveries already made, and are thereby ena- 
bled with joint labour, and an exact conformity of no- 
tions, to carry on the improve?nent of this branch of 
knowledge. And if men in other parts of learning, 
were alike careful to fix the meaning of their terms, 
the progress of science must be greatly furthered, and 



ELEMENTS OF LOGIC. 7i 

ail those verbal disputes, that now so much interrupt 
the course of our improvement, might be prevented. 

Sec. IV.... Definitions of the Name not always true 
and real Definitions ; 
This then ought to be our first care, when we enter 
upon a design-of illustrating any particular branch of 
study ; to ascertain our ideas, and mark the names by 
which they are expressed. And although definitions of 
words are indeed arbitrary, (for a man may affix what 
ideas he pleases to his terms, nor can anyone contest 
this liberty with him,) yet it will be proper to conform 
as near^s possible, to common acceptation, that there- 
by our thoughts may find a more easy and ready en- 
trance into the minds of others. If it should now be 
asked, what are the rules of a good definition ; I an- 
swer, that as in definitions of the name, we aim at no 
more than teaching the connexion of words and ideas ; 
every contrivance, by which we are enabled ^o excite 
the ideas annexed to any word in tlie mind of another, 
will serve the purpose of a definition. Now the idt; ..; 
we join with our words are of two kinds: either such 
as we have reason to believe are already in the minds of 
other?, though perhaps they know not the names by 
which they are called ; or such as, being new and of our 
own formation, can be no otherwise made known than 
by a description. In the first case, there is no necessii 
ty for laying open the idea itse^^f, because being alreody 
known, any contriva'nce to remind us of it is sufficient 
When we say, for instance, that a clockis an instrument^ 
by which we measure the hours of the day ; it is plain, 
that the idea answering to the word c/ocA:, is not here 
unfolded ; but we being before-hand supposed to have 
an idea of this instrument, are only taught by what 
name it is called. Now m this sense, the names of 
even simple ideas may be defined. For, by saying that 
ZMihite is the colour we observe in snow or milk, heat 
the sensation produced by approaching the fire, we suf- 
nciently make knov/n what ideas we connect with the 
terms, white and heaty which is the true purpose of a 
definition of the name. Hence it appears, that many 

G 



7i '^ELEMENTS OP LOGIC, 

of those explanations of words, which logicians calJ de 
finitions of the name, are not definitions in a true and 
proper sense, that is, such descriptions of ideas, a? 
would serve to excite them in the mind of another, even 
supposing him before wholly unacquainted with them, 
but merely contrivances to remind us of known ideas, 
and teach us the names by which they are called. 

Sec. v.... But only when they coincide with the Deft,- 
nition of the Thing. 

But where the ideas we join with our words, are new 
and of our own formation, there they are to be laid open 
by a description, because, being supposed unknown to 
others, we must first raise them in their minds, before 
they can leani to connect them with any particular 
names. And here it is, that the definition of the name 
coincides with what logicians call, the definition of the 
thing, as in either case we proceed by unfolding the 
idea itself for which the term defined stands. And 
indeed this alone is what constitutes a definition, in 
the true and proper sense of the word, as will appear 
more fully afterwards, when we come to consider the 
terms we use, as referred to the real objects of nature. 
We shall therefore postpone this consideratioh of the 
definition of the name, till we come to treat of the de- 
finition of the thing, when it will more naturally fall 
in our way. It may not, however, be amiss to observe, 
that when we say the definitions of the name are arbi- 
traiy, we mean not that the descriptions of ideas are 
^o too. For every idea having a peculiar appearance 
of its own, by which it is distinguished from all others, 
nothing is more evident, than that the description must 
be such as to exhibit that precise conception. But 
then the connexion of any idea, with the name by 
which it is expressed, being, as we have said, wholly 
arbitrary, the considering the description of that idea 
as the definition of that particular name must be so too. 
So that although definitions, considered as descriptions 
of our ideas, are steady and invariable, yet the appli- 
cation of them to particular sounds, (which is all that 
we understand by the definition of the name) is wholiy 
a work of our own free choice. 



ELEMENTS OF LOGIC. 7^ 

t5EC. VI,... Definition of Words according to the common, 
use of Language not Arbitrary. 

But secondly, besides considering words as tlie signs 
of our own ideas, we are also very apt, on many occa- 
sions, to refer them to the ideas in the minds of other 
men. Now, to define a term, in this view, is to inves- 
tigate its meaning or acceptation, according to the 
common use of speech. Here then it is plain, that de- 
imitions are not arbitrary. For although in regarding; 
words as the marks of our own ideas, we may give {hem 
what meaning we please ; yet when we consider then; 
in reference to the thoughts of others, they have a fix 
ed and steady signification ; namely, that which cn^ioin 
and the propriety of language has assigned ther,. The 
w Olds f ability Rnd genius, msij^hy any man, be madf 
to stand for one and the same idea in 'his own mind, 
and if he takes care to advertise us of thi>, Le is at W 
berty to use them prGmiscuousj3\ But if the coiiimofi 
course of language hath confined the word genius to 
express the natural strength and talents; of the nii!i(i 
and the word ability to denote those which are acquir 
ed, whoever pretends to explain the proper acceptatioii 
of these terms, is bound to take notice of this ditler- 
ence. As propriety of speech makes our language in- 
telligible, and gives our thoughts a ready entrance into 
the minds of others, it w^ell deserves cur application and 
care. The best way to acquire it is from the writ- 
ings and discourses of those who seem to have had the 
clearest notions, and to have applied their terms with 
the exactest choice and fitness. 

Sec. VII Definitions of the Thing refer to the real 

Objects of Nature, 
We come now to the third and last species of defini- 
tion, that namely, which considers words as referred to 
things themselves. And here it is plain, we are not at 
liberty to feign and fashion our explications at pleasure, 
but being tied down to the real objects of nature must 
study a conformity to things themselves. When we 
define, for instance, the sun, considered as that being 
who possesses the centre of our system, and difFu=es 



I-Q ELEMENTS OF LOGIG.- 

feeat and light to the planets around him ; it is nai 
enough that we give an. acQOunt of the idea, answer- 
ing to that word in our minds. We must further 
take care^ that the idea itself carries in it a real con- 
formity to the object it is supposed to represent. And 
hence it is, that all definitions of this kind, when just- 
iy made, are in reality pictures or representations, ta- 
ken from the being and existence of things. For they 
are intended to express their nature and properties so 
as to distinguish them from all others, and exhibit, 
them clearly to the view of the mind.. Tis for this 
reason that logicians call them definitions of things, 
because they are supposed to refer, not so much to the 
ideas in the understanding, as to the things themselves 
represented by those ideas. 

Sec. viii... .Ground of the distinction between the de- 
finition of the Name and of the Thing. 

And this also lets us into the ground of that distinc- 
lion so universally received between definitions of the 
name and of the thing. The first are arbitrary, and 
not liablie to debate or contradiction. The second are 
propositions, capable of proof and illustration, and 
which maj^ therefore be contested. The reason is ob- 
vious. Definitions of the name serve only to marii what 
ideas we connect with, our words. And as sounds are 
of themselves indifferent to signif}^ any ideas, we are en- 
tirely at liberty to affix to them what notions we please 
But it is otherwise in the definition of" the thing. For 
iiere our words serving- to denote particular beings in- 
nature, cannot be the signs of any ideas at pleasure, but 
of such only as carry in them a conformity to the sever- 
al objects tow h ich- the words refer. A man may use 
the term, square^ to express that idea, vvhich others de- 
note by the word, triangle, and define it accordingly.. 
In this case, indeed, he recedes from the GGmmon hvms 
of speech, but his definition cannot be charged with 
falsehood. He tells us that by a square he means a 
three-sided figure ; and who can dispute the treth of" 
this, if he really all along uses the word in that sense '^'■ 
\ would only observe, that by changing thus the meaii' 



ELEMENTS OF LOGIC. 77 

mg of words we change not things themselves, or their 
relations and habitudes one towards another. These 
are at all times the same and invariable, nor have any de- 
pendence upon the fancy and caprice of men. It is true, 
the properties of the triangle may, after this definition, 
be affirmed of the square ; but as in either case, the idea 
to which these properties belong, is the same, the pro- 
positions only expressing our judgments, and not our 
judgments themselves, suffer a seeming variation^ 

Sec. IX. ...a previous connexion between J^'ames and 
Things, cuts off all Arbitrary Explications. 
But where words are made to denote particular ob- 
jects, previous to any definitions given, there arbitrary 
explications cannot have place. For in this case, we 
are not put upon explaining what ideas we connect with, 
our words, but a connexion being already supposed be- 
tween the name and the thing signified, our business 
is to unfold that idea by which the object itself is most 
clearly and distinctly represented. Thus the word gold 
denotes that metal which is of highest value among men, 
and goes farthest in the way of commerce. This con- 
nexion being once settled, we are no longer left to ar- 
bitraiy definitions, but must describe it by such proper- 
ties as are really to be found in it, and will best serve to 
distinguish it when it comes in our way ; as by saying it 
is a substance yellov/,very heavy, malleable, fusible, &c.. 

Sec. yi,...Why Mathematical Definitions have been ac- 
counted mere Definitions of the Name ; 
From what has been said, it appears, that in- the lan- 
guage of logicians^ definitions of the thing respect only 
substances and beings that have a real existence in na- 
ture, serving to describe them by their properties and 
attributes. And this, I doubt not, is the reason, that 
the definitions of the mathematicians are not consider- 
ed as definitions of the thing, butof thr, name ; because 
the ideas therein described, are the mere creatures of 
the understanding, and not supposed to be copied from- 
patterns existing without us. A circle, a triangle, a 
square, he. such as mathematicians conceive them, are 
ISO where to be found in nature, that vve know of, 
G 2. 



78 ELEMENTS OF LOGIC. 

Hence it might justly be accounted absurd, to call our 
definitions of these, definitions of the thing, when they 
serve not to describe any real objects of nature, but 
merely to unfold the conceptions of the mind. And 
yet if we look into the matter narrowly, we shall find, 
that the rules followed in these definitions are precisely 
the same with those which logicians have laid down 
iar the definition of the thing. All the several species 
of figures are described by their properties, some of 
which are common to different ranks, others peculiar 
to the tribe defined. The common properties consti- 
tute what logicians call the genus, and those that are 
peculiar, the difference. Now the genus and differ- 
ence make up the logical definition of the thrng, as will 
be more clearly understood from what follows. 

Sec. XI..., When yet they coincide with the logical deff- 
nition of the thing, and therefore ovgkt not to be ac- 
counted arbitrary.. 

I am therefore, apt to think, that mathematical 
definitions, as they are of the same general with the 
definitions of substances, and subject to the same rules„ 
have been improperly considered as mere definitions of 
the name, in which we are left wholly to arbitrary 
explications. For however we may change the name 
ofone figure for another in discourse or writing, using 
the term square to denote a triangle^ or the word tri- 
angle to expressi a square, it is certain the ideas them- 
selves are invariable,, and no less capable of being 
distinguished by their properties, than the several spe- 
' ies of substances. Tl^us if we suppose the word 
square to denote that species of figures, whose sides 
severally subtend quadrants of a circumscribed circle,, 
we shall find ourselves equally shut out from arbitrary 
explications, as in the definition of the names of sub- 
stances. For ?iB this happens in no figures but those 
vvhich are bounded by four equal sides joined together 
at right angles ;. it follows evidently, that the true and 
proper definition of a square, is that which exhibits 
the precise idea here mentioned, and no other, to the 
itnindc And thus it appears, that the common di vision 



ELEMENTS OF LOGIC. 79 

of definitions, into those of the name and thing, is not 
sufficiently calculated to give us right apprehensions, 
as to what is and what is not arbitrary in the explica- 
tion of words. It may not, therefore, be improper, if 
we here endeavour to clear up this matter a little, and 
free it from those obscurities in which it has hitherto 
bei;n involved. To this end we shall premise the fol- 
lowing observations. 

Sic* xu,,.. Definitions, properly speaking, never regard 
Things, but merely our own Ideas. 

1. First, that whatever logicans may pretend about 
the definition of the thing, it is yet certain, that none 
of our definitions, when pursued to their source, regard 
immediately things themselves, but merely the ideas 
in our own minds. This, I doubt not, will appear a 
paradox to many, who will be apt to inquire, whether 
the definition of gold, be not taken from that metal, 
independent of the various conceptions of men about 
it. To this I answer, that indeed in framing our idea 
of gold, we regard chiefly the thing itself, uniting in 
our conception such properties as are most conspicuous, 
and serve best to distinguish it from other metals, to 
which it may bear any resemblance. But as it is by this 
idea alone that gold is known to us, so in describing it 
to others, we aim at nothing more than to transfer the 
same conception into their minds. Now this can no 
otherwise be done, but by enumerating the several pro- 
perties of which our own complex notion is formed. 
And indeed it were in the highest degree absurd to ima- 
gine, that m-en in explaining things to others, should 
make use ofany mark» or characters but those by which 
they are known to themselves. Hence it comes to pass 
that ail our definitions are in fact nothing else but tran- 
scripts of the ideas in our minds. Where these are im- 
perfect, the defi.nitions must be so too ; where they are 
just and adequate, the copies taken from^hem, if drawn 
out with accuracy and care, cannot fail to exhibit the 
object described. .And this will very well serve to ac- 
count for that great diversity of definitions we often 
meet with, even of one and the same object. Because 



dO ELEMEiVTS 01^ LOGIC. 

meft, in consequence of their different pursuits and ap- 
plications, falling often into different views of things 
must needs vary no less in their definitions than in the 
ideas themselves from v/hich these definitions are copi- 
ed. He whose observation goes no farther than the 
more obvious qualities of gold, will content himself 
with describing it by its colour, weight, and perhaps 
malleability and fusibility. On the other hand, a 
goldsmith, having inquired farther into the nature 
of that metal', and finding several other properties that 
equally belong to it, will be apt to take these also into 
his complex idea, and accordingly introduce tliem in a 
definition. Hence his description will add to the form- 
er, fixedness, and solubility in aqua regia, &c. And so 
in proportion, as men's various pursuits lead them inta 
a more accurate examination of things, their explica- 
tions will take a different turn, suitable to the ideas 
they have framed within themselves. 

Sec. xui.... Distinction hetivcen the Dejinitimi of the 
name and thing useless, and to he rejected. 

2. This then being evident, that our definitions re- 
spect not things themselves, bwt the ideas in our own 
minds ; I would in the next place observe, that the dis- 
tinction of them into those of the name and thing, is 
altogether useless, and tends rather to mislead us tlian 
give right apprehensions of the subject in hand. For 
thus men are apt to fancy, that many of their defini- 
tions are expressive of the real essence of things, where- 
as they are in truth no more than transcripts of their 
own ideas. And as it sometimes falls out, that these 
ideas are not collected with sufficient care, from the 
objects they represent ; we find, by experience, that a 
mistaken idea never fails to occasion a mistake also in 
t'he definition. But this could not happen, were our 
definitions copied from things themselves : l>ecause their- 
essences being immutable and always the same, the defi- 
nition would in this case serve to correct the idea, and 
might be considered a& a standard, by Vt^hich. to judge 
whether the idea was rightly. framed. I deny not, that 
words are often transferred from our ideas to signify the 
©bjects which these ideas represent ; as when we talk 



ELEMENTS OF LOGIC. 8^1 

ot the sun, the earth, men, and other animals. But 
then let it be observed, that as these objects are only- 
known to us, by the ideas of them in our minds ; so, ia 
describing them to others, all we aim at is, distinctly 
to lay open our conceptions about them. Hence it 
appears, that what logicians call a definition of the 
thing, is in truth no more than an unfolding of the 
idea, by which that thing is represented to the under- 
standing. But now in mathematical definitions, and in- 
deed all others whatsoever, this also is our whole aim and 
intent, to exhibit and lay open those ideas, of which 
the words we use are sigas. And thus it happens, 
that in innumerable instances, what logicians call the 
definition of the name, is yet found to coincide with 
and proceed by the very same rules, as the definition of 
the thing ; which clearly demonstrates the necessity of 
lianishing this frivolous distinction, and establishing 
some precise and determinate notions, expressive of the 
true nature of a definition, and comprehending it in its^ 
full extent. 

Sec. xiv,...,.D'eJinitio7is in all cases descrijjtions of 
our Ideas. 

Nor will this appear so difficult a task, if we call to 
rnind;,. that words are ia all cases the signs of our idsas, 
and ne otherwise signify things, than as they stand 
for those ideas by which things are represented to the 
understanding. By defining our words, therefore, we 
can mean no more, than the laying open to the view 
of others, the ideas of which these words are the signs. 
For thus it is, thnt the meaning of our expressions 
comes to be known, and that we find ourselves capable 
of transferring our thoughts and conceptions into the 
niin is of those with whom we converse. Where words 
are ret'erred to things themselves, there v/e explain the 
ideas by which these things are represented ; where 
they denote conceptions t'ramed by the mind, there we 
lay open these . conceptions, and endeavour to exhibit 
them according to their real appearance within our 
own breasts. But in both cases, it is our own ideas, 
it Is the perceptions of QiiT own minds, either as taken 



82 ELEMENTS OP LOGIC. 

from things without, or framed by the undestandiBg; 
itself, that we explicate and unfold. 

Sec. XV JVot arhiirary^ as being confined to the 

Ptepre saltation of certain determinate Notions, 
And thus we have at length settled the true and ge- 
nuine notion of a definition, comprehending all its va- 
rieties, from whatever science taken, or to whatever 
object extended. For from what we have said, it evi- 
dently follows, that a definition is the unfolding of 
same conception of the mind, answering to the word or 
term made use of as the sign of it. Now, as in exhi- 
biting any idea to another, it is necessary that the de- 
scription be such as may excite that precise idea in 
his mind ; hence it is plain, that definitions, proper- 
ly speaking, are not arbitrary, but confined to the re- 
presenting of certain determinate settled notions, such, 
namely, as are annexed by the speaker or v/riter to 
the words he uses. As, nevertheless, it is universally 
allowed, that the signification of words is perfectly vo» 
luntary, and not the effect of any natural and necessary 
connexion between them and the ideas for which they 
stand, some may perhaps wonder why definitions are 
not so too. In order, therefore, to unravel this diffi- 
culty, and show distinctly what is, and what is not ar- 
bitrary in speech we, must carefully distinguish be- 
tween, the connexion of our words and ideas, and the 
Pinfolding of the ideas themselves. 

3ec. XVI. ...The Connexion between Words and Ideas, 
a perfectly voluntary Establishment. 
First, as to the connexion of our words and ideas^ 
this, it is plain, is a purely arbitrary institution. When 
for instance, we' have in our minds, the idea of any 
particular species of metals, the calling it by the name 
gold, is an effect of the voluntary choice of men speak- 
ing the same language, and not of any peculiar apt- 
ness in that sound to express that idea. Other nations, 
we find, make use of different sounds, and with the 
game effect. Thus aurum denotes that idea in Latin » 
an^' or in Frencli, And even the word gold itself, 
vrpuld have as well served to express the idea of that 



ELEMENTS O? LOGIC, B3 

metal which ive call silver, had custom in the beginning 
so established it. 

Sec. xvu.,..The Descriptions of Ideas not so, but bound- 
ed to the Representation of that precise Appearance. by 
which they are distinguished among themselves. 

But although we are thus entirely at liberty, in 
connecting any idea with any sound, yet it is quite 
otherwise in unfolding the ideas themselves. For eve- 
ry idea, having a precise appearance of its own, by 
which it is distinguished from every other idea ; it is 
manifest, that in laying it open to others, we must 
study such a description, as shall exhibit that peculiar 
appearance. When we have formed to ourselves the 
idea of a figure bounded by four equal sides, joined to- 
gether at right angles, we are at liberty to express that 
idea by any sound, and may call it either a square or a 
triangle. But which ever of these names we use, so 
long as the idea is the same, the description by which 
we would signify it to another, must be so too. Let 
it be called sgware or triangle, it is still a figure hav- 
ing four equal sides, and all its angles right ones. 
Hence we clearly see, what is and what is not arbitrary 
in the use of words. The establishing any sound, as 
the mark of some determinate idea in the mind, is the 
effect of free choice, and a voluntary combinaton a- 
mong men. And as different nations make use of 
different sounds, to denote the same ideas, hence pro- 
ceeds all that variety of languages which we meet with 
in the world. But when a connexion between our 
ideas and words is once settled, the unfolding of the 
idea answering to any word, which properly consti- 
tutes a definition, is by no means an arbttr iry thing. 
For here, as I have already observed, we are bound to 
exhibit that precise conception, which either the use 
oflanguago or our own particular choice, hath annex- 
ed to the term we use. 



-84 ele'Ments of LOiilC* 

Sec. xvni.. ..Causes of the Obscurity that has hithert&' 
perplexed the Theory of Definitions. 

And thus it appears, that definitions, considered as 
descriptions of ideas in the mind, are steady and inva- 
riable, being bounded to the repi-esentation of those 
precise ideas. But then in the application of definitions 
to particular names, we are altogether left to our own 
free choice. Because as the connecting of any idea 
with any sound is a perfectly arbitrary institution ; 
the applying the description of that idea, to that 
sound must be so too. When, therefore, logicians tell 
us, that the definition of the name is arbitrary, they 
mean no more than this ; that as different ideas may 
be connected with any term, according to the good 
pleasure of him that uses it, in like manner may differ- 
ent descriptions be applied to that term, suitable to 
the ideas so connected. But this connexion being set- 
tled, and the term considered as the sign of some fixed 
itiea in the understanding, we are no longer left to ar- 
bitrary explications, but must study such a descrip- 
tion as corresponds with that precise idea. Now this 
alone according to what has been before laid down, 
©light to be accounted a definition. What, I am apt 
to think, has occasioned no small confusion in this 
matter is, that many explanations of words, where no 
idea is unfolded, but merely the connexion between 
some word and idea asserted, have yet been dignified 
with the name of definitions. Thus in the instance 
before given, when we say that a clock is an instru- 
ment by which we measure time, this is by some called 
a definition. And yet it is plain, that we are before- 
hand supposed to have an idea of this instrument, and 
only taught that the word clocks serves in common 
language to denote that idea. By this rule all expli- 
cations of words in our dictionaries will be definitions ; 
nay as was already observed, the names of even sam- 
ple ideas may be thus defined. JF/tiYe we may say, is 
the colour we observe in snow or milk, heat the sen- 
sation produced by approaching the fire, and so in in- 
numerable other instances. But these, and all others 



ELEMENTS OF LOGIC. 85 

j:" the like kind, are by no means definitions, exciting 
new ideas in the understanding, but merely contri- 
vances to remind us of known ideas, and teach their 
-connexion with the established names. It is, neverthe- 
less, worth our notice, that what logicians call deli- 
nitons of the name, extend properly no farther than 
these explanations, serving to mark the connexion of 
our ideas and words, and are therefore justly account- 
ed arbitrary, inasmuch as the connexions themselves 
are altogether so. 

Sec. X'ix.,.,.Co?7jj9lc.'r ideas alom capable of tJutt kind 
of description which goes by the name of a definition. 

But now in definitions properly so called, we first 
consider the term we use, as the sign of some inward 
€t)nceptiGn, either annexed to it by custom, or our own 
Tree choice ; and then the business of the definition is 
to unfold and explicate that idea. As therefore the 
whole art lies, in giving just and true copies of our 
ideas, a definition is then said to be perfect, when it 
serves distinctly to excite the idea described in the 
mind of another, even supposing him before wholly un- 
acquainted with it. This point settled, let us next in- 
<4uire into what those ideas are which are capable of 
being thus unfolded. And in the first place, it is 
evident, that aU our simple ideas are necessarily ex- 
cluded. We have seen already, that experience alone 
is to be consulted here, insomuch, that if either the 
objects, whence they are derived, come not in our way, 
or the avenues appointed by nature for their receptiort 
are wanting^ no description is sufficietit to convey them 
into the mind. But where the understanding is aJrea- 
dy supplied with these original and primitive concep- 
tions, as they may be united together in an infinity of 
different forms ; so may ail their several combinations 
be distinctly laid open by enumerating the simple idea* 
concerned in the various collections, and tracing the 
order and manner in which they are linked one to anc^ 
tlier. Now these combinations of simple notices con- 
stitute what we call our complex notions ; whence it i,-: 
evident that complex ideas, and those alone, admit of 

n 



<T6 ELEIrlENTS OF LOGIC, 

that kind of description, which goes by the name otii 
definition. 

Sec. XX.... Iflieii a complex idea may be said to be Jul- 
ly unfolded. 

The business of definitions is now, I think, pretty 
plain. They are, as we have seen, pictures or repre- 
sentations of our ideas ; and as these representations 
are then only possible, when the ideas themselves are 
complex ; it is obvious to remark, that definitions can- 
not have place, but wliere we make use of terms, 
standing for such complex ideas. But perhaps the rea- 
der may still expect, that we should enter a little more 
particularly into the nature of a definition, describe its 
parts, and show by what rules \i ought to proceed, in 
order to the attainment of its proper end. To give, 
therefore, what satisfaction we are able upon this point, 
we must again call to mind, that the design of a defini- 
tion is, so to unfold the idea answering to any term, as 
that it may be clearly and distinctly transferred into 
the mind of another. But now our complex ideas, 
which alone are capable of this kind of description, 
being, as we have said, nothing more than different 
combinations of simple ideas ; we then know and com- 
prehend them perfectly, when we know the several 
simple ideas of which they consist, and can so put them 
together in our minds, as is necessary towards the 
framing of that peculiar connexion, which gives every 
idea its distinct and proper appearance. 

Sec. 'KXi....Two things required in a dejinition ; to 
enumerate the ideas, and explain the manner of their 
combinations. 

Two things are therefore required in every defini- 
tion. First, that all the original ideas, out of which 
the complex one is formed, be distinctly enumerated. 
Secondly, that the order and manner of combining 
them into one conception, be clearly explained. Where 
a definition has these requisites, nothing is wanting to 
its perfection ; because every one who reads it and un- 
derstands the terms, seeing at once what ideas he is 
to join together, and also in what manner, can at plea- 



ELEMENTS OF LOGIC. 87 

scire form in his, own mind the complex conception 
answering to the term defined. Let us, for instance, 
f suppose the word, square, to stand for that idea, by 
which we represent to ourselves a figure whose sides 
subtend quadrants of a circumscribed circle. The parts 
of this idea^ are the sides bounding the figure. These 
must be four in number, and ail equal among them 
selves, because they are -each to subtend a fourth part 
of the same circle. But besides these coifiponenf 
parts, we must also take notice of the manner of put- 
ting them together, if we would exhibit the precise 
idea, for u'hich the word sqraare here stands. For four 
equal right lines, any how joined, will not subtend 
quadrants of a circumscribed circle. A figure witii 
this property, must have its sides standing also a; 
right angles. Taking in therefore, this last considv- 
ration, respecting the manner of combining tlie part.-, 
the idea is fully described, and the definition thereby 
rendered ccmpletc. For a figure, bounded by four 
equal sides, joined together at right angles, has the 
property required ; and is, moreover, the only right 
uned figure to v.hich that property belongs. 

5zc. y:ni....i/o'^) rcc arc to proceed to arrive at just 
and adequate definitions. 

And r.ow, 1 imagine, it will be obvious to ever}' 
one in what manner we ought to proceed, in order to 
arrive at just and adequate definitions. First, wc are 
to take an exact view of the idea to be described, trace 
it to its original principles, and mark the several sim- 
})le perceptions that enter into the composition of it. 
Secondly, we are to consider the particular manner in 
which these elementary ideas are combined, in order to 
the forming of that precise conception, for whi-:h the 
term we make use of stands. When this is done, and 
the idea wholly unravelled, we have nothing more to 
do than fairly transcribe the appearance it makes to 
our own minds. Such a description, by distinctly ex- 
hibiting the order and number of our primitive con- 
ceptions, cannot fail to excite, at the same iime, in the 
xaind of every one that reads it the complex idea re- 



88> ELEMENTS OF LGGiG. 

suiting from them ; and therefore attains the true and 
proper end of a definition. 



CHAP. VII. 

OF THE COMPOSITION AND RESOLUTION OF OUR IDEASj 
AND THE RULES OF DEFINITION THENCE ARISING. 



Sec. I.. ..In compounding our Ideas, we proceed by sitc- 
cessive gradation. 

The rulcj^ laid down in the foregoing chapter, b 
general, extending to all possible cases ; and is, 
indeed, that to which alone we can have recourse, 
wrhereany doubt op difficulty arises. It is not, how- 
ever, necessary, that we should practise it in every par- 
ticular instance Many of our ideas^ are extremely 
complicated ; insomuch that to enumerate all the sim- 
ple perceptions out of which they are formed, would be 
a very troublesome and tedious work. For this rea- 
son, logicians have established certain compendious, 
rules of defining, of which it may not be amiss here to 
,f^ive some account. But in order to the better under- 
standing of what follows, it will be necessary to ob- 
serve, that there is a certain gradation in the com- 
t osi'ion of our ideas,^ The mind of man is veiy li- 
mited ia its views, and canaot take in a great number 
of objects at once. We are, therefore, fain to proceed 
by steps, and make our first advances subservient to 
ruose which follow. Thus in forming our complex 
notions, we begin at first with but a few simple ideas^ 
:-uch as we can manage with ease, and unite them to- 
gether into one conception. When we are provided 
with a sufiieient stock of these,, and have, by habit 
and use, rendered them familiar to our minds, they be- 
come the component parts of other ideas, still more 
complicated, and form what we may call a second or- 
der of compound notions. This process, as is evident- 
.may be continued, to any degree of composition we 



ELEMENTS OF LOGIC. 8D 

please, mounting from one stage to another, and en- 
larging the number of combinations. 
Sec. II. ...Hence ideas of this class best comprehend^ 

when we advance gradually through all the several 

orders. 

But nou' in a series of this kind, whoever would 
acquaint himself perfectly with the last and highest 
order of ideas, finds it much the most expeditious me- 
thod,, to proceed graduall}'- through all the intermedi- 
ate steps. For was he to take any very compounded 
idea to pieces, and without regard to the several 
classes of simple perceptions, that have already been 
formed into distinct combinations, break in at once 
into its original principles, the number would be so 
great, as perfectly to confound the imagination, and 
overcome the utmost reach and capacity of the mind. 
When we see a prodigious multitude of men, jumbled 
together in crowds, without order, or any regular po- 
sition, we find it impossible to arrive at an exact know- 
ledge of their number. But if they are formed into 
separate battalions, and so stationed as to fall within 
the leisurely survey of the eye ; by viewing them succes- 
.sively and in order, we come to an easy and certain de- 
lermination. It is the same in our complex ideas. 
When the original perceptions, out of which they are 
framed, are very numerous, it is not enough that we 
lake a view of them in loose and scattered bodies. We 
must form them into distinct classes, and unite these 
classes in a just and orderly manner, before we can ar- 
rive at a true knowledge of the compound- notices re- 
sulting from them. 

Sec. in.. ..Our Definitiom ought to keep pace without 
Ideas^ and observe a like gradation . 
This gradual progress of the mmd to its compound;- 
notions, through a variety of interm.ediate^ steps, plain- 
ly points out the manner of conducting the definitions 
by v/hich these notions are convej'-ed into the minds of 
others. For as the series begins with simple and easy 
combinations, and advances througii a succession ot 
different orders, rising one above another in the de- 
cree of composition jit is evident, that in a train cfdp- 
H2 



90 -'^ ELEMENTS OF LOGIC* 

fmitions expressing^ these ideas, a like gradatron is to 
be observed. Thus the complex ideas of the lowest or- 
der, can no otherwise be described, than by enumerat- 
ing the simple ideas out of which they are made, and 
explaining the manner of their union. But then in 
the second, or any succeeding order, as they are form- 
ed out of those gradual combinations, that constitute 
the inferior classes, it is not necessary in describing 
them, to mention one by one, all the simple ideas of 
which they consist. They may be more distinctly and 
briefly unfolded, by enumerating the compound ideas of 
a lower order from whose union they result, and which 
are all supposed to be already known, in consequence of 
previous definitions. Here then it is that the logical 
method of defining takes place ; which that we may the 
]3etter understand, I shall explain somewhat more par- 
ticularly, the several steps and gradations of the mind, 
in compounding its ideas, and thence deduce that pecu- 
liar form of a definition, which logicians have thouhgt 
tit to establish. 

Sec. IV.... The steps by which the Mmd proceeds Jrorn 
Particular to General Ideas. 
All the ideas we receive, from the several objects of 
mature that surround us, represent distinct individuals. 
These individuals, when compared together, are found 
m certain particulars to resemble. Hence, by collect- 
ing the resembling particulars} into one conception, we 
ibrm the notion of a species. And here let it be ob- 
served, that this last idea is less complicated than that 
by which we represent any of the particular objects 
contained under it. For the idea of the species ex- 
cludes the peculiarities of the several individuals, and 
retains only such properties as are common to them all. 
Again^ by comparing several species together, and ob» 
serving their resemblance, we form the idea of the 
^enus ; where, in the same manner as before, the com- 
position, is lessened, because we leave out what is pecu- 
liar to the several species compared, and retain only the 
particulars wherein they agree. It is easy to conceive 
the mind proceeding thus from one step to another, 
and advancing through its several classes of general no- 



ELEMENTS OF LOGIC. 91 

t:6ns, until at last it comes to the hi^iiest genus of 
all, denoted by the word being, where the bare idea of 
existence is only concerned. 

Sec. v....TIie conduct of the Mindin compounding its 
Ideas, as it advances through the different orders of 
perception. 

In this procedure, we see the mind unravelling a 
complex idea, and tracing it in the ascending scale, from 
greater to less degrees of composition, until it termi- 
nates in one simple perception. If nov/ we take the 
series the contrary way, and beginning with the last 
or highest genus, carry our view downwards, through 
all the inferior genera and species, quite to the indivi- 
duals ; we shall thereby arrive at a distinct apprehen- 
sion of the conduct of the understanding in compound- 
ing its ideas. For in the several classes of our per- 
ceptions, the highest in the scale is, for the most part, 
made up of but a few simple ideas, such as the mind 
can take in and survey with ease. This first general 
notion, when branched out into the different subdivi- 
sions contained under it, has in every one of them 
something peculiar, by which they are distinguished 
among themselves ; insomuch that in descending from 
the genus to the species, we always superadd some 
new idea, and thereby increase the degree of composi- 
tion. Thus the idea denoted by the woidi Jigure, is 
of a very general nature, and composed of but few sim- 
ple perceptions, as implying no more than space every 
where bounded. But if we descend farther, and con- 
sider the boundaries of this space, as, that they may 
be either lines or surfaces, we fall into the several spe- 
cies of figure. For where the space is bounded by one 
or more surfaces, we give it the name of a solid figure ; 
but where the boundaries are lines, it is called a plain 
figure. 

Sec vi....77ie Idea of the Species formed by superadd- 
ding the specific Difference to the Genus. 
In this view of things, it is evident, that the spe- 
cies are formed by superadding a new idea to the genus: 
Here J for instance, the genu5 is circumscribed space. 



qrr 



ELEMENT3 OF LOGIC. 



If now to this we superadd the idea of a circumscrip- 
tion by line, we frame the notion of that species of 
%ures which are calledjs/cfm; but if we conceive the 
~ circumscription to be by surfaces, we have the spe- 
cies of solid figures. This superadded idea is called 
the specific difference^ not only as it serves to divide 
the species from the genus, but because, being differ- 
ent in all the several subdivisions, we thereby also dis- 
tinguish the species one from another. And as it is 
likewise that conception, which, by being joined to 
the general idea, completes the notion of the species ; 
hence it is plain, that the genus and specific difference 
are to be considered as the proper and constituent parts 
of the species. If we trace the progress of the mind 
still farther, and observe it advancing through the in- 
lerior species, we shall find its manner of proceeding 
to be always the same. For every lower species is 
ibrmed by superadding some new idea to the species 
next above it ; insomuch, that in descending the scale 
of our perceptions, the understanding passes through 
different orders of complex notions, which become more 
and more complicated at every step it takes. Let us 
resume here, for instance, the species of plain figures- 
They imply no more than space bounded by lines. 
But if we take in an additional consideration of the 
nature of these lines, as, whether they are right or 
curves, we fall into the subdivisions of plain figure, 
distinguished by the names rectilinear, curvilinear and- 
mioctilinear. 

Sec. V 11.... And in all the inferior species by superad- 
ding the specific to the nearest genus. 
And here we are to observe, that though plaia 
figures, when considered as one of those branches that 
eome under the notion of figure in general, take the 
name of a species ; yet compared with the classes of 
curvilinear, rectilinear, and mixtilinear, into which 
they themselves may be divided, they, really become a 
genus, of which the before-mentioned subdivisions con- 
Mitute the several species. These species, in the^ame 
manner as in the case of plain and solid figures, cor/- 
3i#t-of the genus and specific difference, as their coHs- 



ELEMENTS OF LOGIC. do 

&tjtu6nt parls. For in the curvilinear kind, the cur- 
viiyodhe lines bounding the figure, makes what is 
called the specific difference ; to which if we join the 
genus, which here is plain figure, or space circumscrib- 
ed by lines, we have all that is necessary towards com- 
pleting the notion of the species. We are only to 
take notice, that this last subdivision, having two ge- 
nera above it, viz, -plain figure^ tiyi^l figure in general ; 
the genus, joined with the specific diiference, in order 
to constitute the species oi curvilinear ^ is that which 
lies nearest to the said species. It is the notion of 
plain figure^ and not oi figure in general^ that joined 
with the idea oicurvity^ makes up the complex con- 
ception oi curve-lined figures. For in this descending 
scale of our ideas— H^wre in general, plain figures^, 
curve-lined fi.gures — the two first are considered as ge- 
nera in respect to the third ; and the second in order^ 
or that which stands next to the third, is called the 
nearest genus. But now as it is this second idea, 
which, joined with the notion of curvity^{ovm% the spe- 
cies o{ curve-lined figures ; it is plain, that the third or 
last idea in the series, is made tip of the nearest genus 
and specific difference. This rule holds invariably, 
however fiir the series is continued ; because in a train 
of ideas thus succeeding one another, all that precede 
the last are considered as so many genera, in respect of 
that lust ; and the last itself is always formed, b}^ su- 
peradding the specific diuerence to the genus next it. 

*^EC. xiu....Theideaof an indtvidiial composed of the 
lowest species and numeric difference. 

Here then we have an universal description, applica- 
ble to all oiU' ideas, of whatever kind, from the high- 
est genus, to the lowest species. For trrking them in 
order downwards from the said general idea, they eve- 
vy where consist of the genus proximum, 2Lnd. differen- 
tia specifica, as logicians love to express themselves. 
But when we come to the lowest species of all, com- 
prehending in it only individuals, the superadded idea, 
l)y \yhich these individuals are distinguished one from 
'another, no longer takes the name of the specific diftei"- 



94 ELEMENTS OF LOGIC. 

ence. For here it serves not to denote distinct spe- 
cies, but merely a variety of individuals, each of wb^ch 
having a particular existence of its own, is therefore 
numerically different from every other of the same 
kind. And hence it is, that in this last case, logi- 
cians choose to call the superadded idea by the name of 
the numerical difference ; insomuch that as the idea of 
a species, is made up oi \\ie, nearest genus 2.n(i specijic 
difference, so the idea of an individual cousists of the 
lowest species and numeric difference. Thus the circle 
is a species of curve-lined figures, and what we call the 
I oii-est species, as comprehending under it only indivi- 
duals. Circles in particular are distinguished from one 
another by the length and position of their diameter:. 
The length, therefore, and position of the diameter of 
a circle, is v/hat logicians call the numerical differ- 
ence ; because these being given, the circle itself may 
be described, and an individual thereby constituted. 

Se€. IX Definitions to follow one another in train, 

and pass through the same successive gradations as 
our compound ideas. 

And thus we have endeavoured to trace, in the best 
manner we are able, the progress of the mind in com- 
pounding its ideas. It begins, we see, with the most 
general notions, which consisting of but a few simple 
notices, are easily combined and brought together into 
one conception. Thence it proceeds to the species com- 
prehended under this general idea, and these are form- 
ed by joining together the genus and specific difference. 
And as it often happens, that these species may be still 
further subdivided, and run on in a long series of con- 
tinued gradations, producing various orders of com- 
pound perceptions ; so all these several orders are regu 
Jarly and successively formed, by annexing in every step, 
the specific difference to the nearest genus. , When by this 
method of procedure, we are come to the lowest order 
of all ; by joining the species and numeric differ ence ^w a 
frame the ideas of individual*. And here the series ne- 
cessarily terminates, because it is impossible diWj farther 
to bound or limit our conceptions. This view of the 



elemeznTS of logic. 95 

composition of our ideas, representing their constituent 
parts in every step of the progression, naturally points 
out the true and genuine form of a definition. For as 
definitions are no more than descriptions of the ideas for 
which the terms defined stand ; and as ideas are then 
described, when we enumerate distinctly and in oider, 
the parts of which they consist ; it is plain that, by 
making our definitions follow one another, according 
to the natural train of our conceptions, they will be sub- 
ject to the same rules, and keep pace with the ideas 
they describe. 

Sec. \..., The form of a Definition in all the various 
orders of conception. 
As therefore the first order of our compound notions 
or the ideas that constitute the highest genera, in the 
different scales of perception, are formed by uniting 
together a certain number of simple notices ; so the 
terms expressing these genera are defined hy enumera- 
ting the simple notices so combined. And as the species 
comprehended under any genus, or the complex ideas 
of the second order, arise from superadding the specific 
difterence to the said general idea ; so the definition of 
the names of the species is absolved, in a detail of the 
ideas of the specific difference^ connected -with the term of 
the genus. For the genus having been before defined, the 
term by which it is expressed stands for a known idea, 
and may therefore be introduced into all subsequent de- 
finitions, in the same manner as th* names of simple 
perceptions. It will now, I think, be sufficiently obvious 
that the definitions of all the s<jcceeding orders of com- 
pound notions, will ever}'' where consist of the term qf 
the nearest genus joined zvith an enumeration of the ideas 
that conUitute the specific difereuce ; and that the defini- 
tion of individuals ^uiites the aCrnie of the lozcest specie^, 
with the terms by zi-hich ve co:pTCSs the ideas of the nu~ 
meric difference. 

Sec. xi....The logical mcihod of defining perfect in its 
kind ; 
Here then we have tiie true and proper form of a 
definition, in all the various orders of conception. 



^6 EXEMEKTS OF LOGIC, 

This is that method of defining, which is commonly 
called logical, and which, we see, is perfect in its kind, 
inasmuch as it presents a full and adequate description 
of the idea, for which the term definedstands. There 
are still two things worthy of observation, before we 
take leave of this subject. First, that the very frame 
and contexture of these definitions, points out the order 
in which they ought to follow one another. For as 
the name of the genus" is admitted into a description, 
only in consequence of its having been before defined ; 
it is evident, that we must pass gradually through all 
the different orders of conception. Accordingly, logi- 
cians lay it down as a rule, that we are to begin always 
with the highest genus, and carry on the series of de- 
finitions regularl}^, through all the intermediate genera 
and species, quite down to the individuals. By this 
means our descriptions keep pace with our ideas, and 
pass through the same successive gradations ; insomuch 
that the perusal of them must excite those ideas in the 
understanding of another, in the very order and man- 
ner in which they are put together by the mind in its 
uniform advances from simple to the most complicated 
notions. Now this is the true and proper end of de- 
fining, and indeed the highest perfection of that art. 

Sec. xu....And applicaUe to all words whatsoever ca- 
pable of a definition. 

There is^ yet another thing to be observed on this 
head, namely, that the form here prescribed, is appli- 
cable to all woids whatsoever, capable of a defini- 
tion. For as every term we use, must denote some idea 
either general or particular ; and aS all our complex 
notions relating to both these classes of perception from 
the highest genus quite down to the individuals, come 
within the rules of description here given ; it is evi- 
dent that this particular manner of unfolding an idea 
may be extended to ail the possible complex concep- 
tions we can connect with our words. Bj the rules 
therefore of this method, definitions may be applied to 
;ill terms standing for complex ideas ; and as these, by 
what we have shown at large in the two foregoing 



ELEMENTS OF LOGIC. 97 

chapters, are the only definable articles of speech ; it 
necessarily follows, that the directions here given are 
universal, extend to all particular instances, and are 
alike applicable in all languages. And thus at length, 
we have not only deduced that peculiar form of a defi- 
nition which obtains among logicians, but shown it 
also to be perfect in its kind, and to take in the whole 
compass of language. 



BOOK II. 

Of Judgment, or Intuition. 

CHAP. I. 

QF THE GROUNDS OF HUWAN JUDGMENT. 



Sec. I Intuition respects the relations between our 

Ideas "when they are immediately perceivable. 

When the mind is furnished with ideas, its next 
step in the way to knowledge is, the comparing 
these ideas together, in order to judge of their agree- 
ment or disagreement. In this joint view of our 

ideas, if the relation is such, as to be immediately dis- 
coverable by the bare inspection of the mind ; the judg- 
ments thence obtained are called intuitive^ from a word 
that denotes to look at : for in this case, a mere atten- 
tion to the ideas compared, suffices to let us see, how 
far they are connected of disjoined. Thus, that the 
•whole is greater than any of its parts^ is an intuitive 
judiraient, nothing more being required, to convince 
us of its truth, than an attention to the ideas of whole 
and part. And thisV too, is the reason, why we call 
I, 



9^8 ELEMENTS OF LOGIC. 

the act of the mind forming these judgments iniuiiion; 
as it is indeed no more than an immediate perception 
of the agreement or disagreement of any two ideas. 

Sec. n... .Experience and Testimony the Ground of 
judging as to Facts. 
But here it is to be observed, that our knowledge of 
this kind, respects only our ideas, and the relations 
between them, and therefore can serve only as a foun- 
dation to such reasonings, as are employed in investi- 
gating these relations. Now it so happens, that many 
of our judgments are conversant about facts, and the 
xeal existence of things which cannot be traced by the 
bare contemplation of our ideas. It does not follow, 
because I have the idea of a circle in my mind, that 
therefore a figure answering to that idea, has a real 
existence in nature. I can form to myself the notion 
ofa centaur, or golden mountain, but never imagine 
on that account, that either of them exists. What 
then are the grounds of our judgments, in relation to 
facts ? I answer, these two : experience and testimony. 
'By experience we are informed of the existence of the 
several objects which surround us, and operate upon 
our senses. Testimony is of a wider extent, and reaches 
not only to objects beyond the present sphere of our 
observation, but also to facts and transactions, which, 
being now past, and having no longer any existence, 
could not, without this conveyance, have fallen under 
our cognizance. 

Sec. Ill Three Foundations of Human Judgment, 

viz. 1. Intuition^ the Ground of scientifix^al know- 
ledge : 

Here then we have three foundations of human 
judgment, from which the whole system of our know- 
ledge may with ease and advantage be deduced. First, 
intuition^ which respects our ideas themselves, and 
their relutions, and is the foundation of that species of 
reasoning, which we call demonstration. For what- 
ever is deduced from our intuitive perceptions, by a 
clear and connected series of proofs, is said to be de- 
monstrated, and produces absolute certainty in the 



ELEMENTS OF LOGIC. 9? 

mind. Hence the knowledge obtained in this manner, 
is what we properly term science ; because, in every 
step of the procedure, it carries its own evidence along 
with it, and leaves no room for doubt or hesitation. 
And what is highly worthy of notice ; as the truths 
of this class express the relations between our ideas, 
and the same relation must ever and invariably sub- 
sist between the same ideas, our deduction, in the way 
of science, constitute what we call eternal, necessary, 
and immutable truths. If it be true, that the whole 
is equal to all its parts, it must be so unchangeably ; 
because the relations of equality being attached to the 
ideas themselves, must ever intervene where the same 
ideas arc compared. Of this nature are ail the truths 
of natural religion, morality, and mathematics ; and in 
general whatever may be gathered from the bare view 
and consideration of our ideas. 

Sec. iv 2. Experience the Ground of our Knoxvledge 

of the PoTvers and Qualities of Bodies. 

The second ground of human judgment is experience ; 
from which we infer the existence of those objects that 
surr-ound us, and fall under the immediate notice of our 
senses. When w^e see the sun, or cast our eyes towards 
a building, we not only have ideas of these objects 
within ourselves, but ascribe to them a real existence 
out of the mind. It is also by the information of the 
senses, that we judge of the qualities of bodies ; as 
v.hen we say that snov/ is white, fire hot, or steel 
hard. For as we are wholly unacquainted with the in- 
ternal structure and constitution of the bodies that 
produce these sensations in us, nay, and are unable to 
trace any connexion between that structure and the 
sensations themselves, it is evident that we build out- 
judgments altogether upon observation, ascribing to 
bodies such qualities as are answerable to the percep- 
tions they excite in us. But this is not the only ad- 
vantage derived from experience, for to that, too, are 
we indebted for all our knowledge regarding the co- 
existence of sensible qualities in objects, and the ope- 
rations of bodies one upon another. Ivory, for in- 



iOO ELEMENTS OF LOGIC. 

stance, is herd and elastic ; this we know by experi- 
ence, and indeed by that alone. For being altogether 
strangers to the true nature both of elasticity and hard- 
ness, we cannot, by the bare contemplation of our 
ideas, determine how far the one necessarily implies 
the other, or whether there may not be a repugnance 
between them. But when we observe them to exist 
both in the same object, we are then assured from 
experience that they are not incompatible ; and when 
we also find, that a stone is hard and not elastic — and 
that air, though elastic, is not hard — we also conclude, 
upon the same foundation, that the ideas are not ne- 
cessarily conjoined, but may exist separately in differ- 
ent objects. In like manner, with regard to the opera- 
tions of bodies, one upon another, it is evident, that 
our knowledge this way is all derived from observa- 
tion. Aqua regia dissolves gold, as has been found by 
frequent trial ; nor is there any other way of arriving 
at the discovery. Naturalists may tell us, if they please, 
(hat the parts of a^i^arc^'a are of a texture apt to in- 
sinuate between the corpuscles of gold, and thereby 
iposen and shake them asunder. If this is a true ac- 
count of the matter, I believe it will, notwithstanding, 
be allowed, that our conjecture, in regard to the con- 
formation of these bodies, is deduced from the experi- 
ment, and not the experiment from the conjecture. It 
was not from any previous knowledge of the intimate 
•structure of aqtia regia and gold, an d the aptness of 
their parts to act or be acted upon, that we came by 
the conclusion above mentioned. The internal consti- 
tution of bodies is in a manner wholly unknown to us : 
and could we even surmount this difficulty, yet as the 
separation of the parts of gold implies something like 
an active force in the menstruum, and we are unable 
to conceive how it comes to be possessed of this acti- 
vity ; the effect must be owned to be altogether beyond 
our comprehension. But^when repeated trials had once 
confirmed it, insomuch that it was admitted as an esta- 
blished truth in natural knowledge, it was then easy 
for men to spin out theories of their own invention, 
and contrive such a structure of parts, both for gold 



ELEMENTS OF LOGIC. 101 

arid aqua regia, as would best serve to explain the 
phenomenon, upon the principles of that system of 
philosophy they had adopted. I might easily show 
from innumerable other instances, how much our 
knowledge of the mutual action of bodies depends upon 
observation. The bite of a viper will kill. Plants are 
some salutary, others noxious. Fire dissolves one body 
and hardens another. These are truths generally 
known ; nor is it less evident that we owe their disco- 
very wholly to experience. 

Sec. v.. ..Why many useful Inventions owe their Birth 
to Chance. 
And hence it is easy to account for what to some 
writers has appeared a very great paradox ; that many 
of the most important inventions in human life have 
taken their rise from chance, and instead of coming- 
out of the schools of philosophers, are for the most 
part ascribed to men of no figure in the commonwealth 
of learning. Sowing, planting, the use of compass, 
and such like, are not deductions of human reason, 
but discoveries which owe their birth to observation 
and trial. No wonder, therefore, if these inventions 
derived their beginning from such a.*?, being engaged 
in the active and busy scenes of life, were more in the 
way of those experiments which lead to discoveries of 
this nature. And here, as the particular callings and 
professions of men, and oft-times chance, has a great 
ascendant, it need not seem strange, if some of the 
most useful arts in society appear to have had an ori- 
ginal purely casual. 

Sec. Yi... .Natural Knowledge, from the grounds on 
-which it rests, aptly termed experimental Philosophy. 
From what has been said, it is evident, that as intui- 
tion is the foundation of what we call scieniifcal 
knowledge ; so is experience of natural. For this last 
being wholly taken up with the objects of sense, or 
those bodies that constitute the natural world— and 
their properties, as far as we can discover them, being 
to be traced only by a long and painful series of obser- 
vations ; it is apparent, that in order to improve this 
1 2 



102 ELEMENTS OP LOGIC. 

branch of knowledge, we must betake ourselves to the 
method of trial and experiment. Accordingly, we find 
that while this was neglected, little advance was made 
in the philosophy of nature ; whereas a contrary pro- 
<:'eeding has enriched the present age with many valu- 
able discoveries ; insomuch that natural knowledge, in 
allusion to the foundation on which it stands, has been 
very aptly called experimental philosophy. 

^EC. \' 11.... Though much of our Knowledge of body 
depends on Testimony, yet Experience is the ulti- 
\ mate Foundation of it. 

But though experience is what we may term the im- 
mediate foundation of natural knowledge, yet with re- 
spect to particular persons, its influence is very nar- 
row and confined. The bodies that surround us are 
numerous ; many of them lie at a great distance ; and 
«ome quite beyond our reach. Life too is short, and 
so crowded with cares, that but little time is left for 
i,x\j single man to employ himself in unfolding the 
mysteries of nature. Hence it is necessary to admit 
many things upon the testimony of others, which, by 
this means, becomes the foundation of a great part of 
our knowledge of body. No man doubts of the power 
of aqua regia to dissolve gold, though perhaps he ne- 
ver himself made the experiment. In these, therefore, 
and such like cases, we judge of the facts, and opera- 
tions of nature, upon the mere ground of testimony. 
However, as we can always have recourse to experi- 
ence, where any doubt or scruple arises, this is justly 
considered as the true foundation of natural philos- 
ophy being indeed the ultimate support upon which our 
assent rests, and v,^hereto we appeal, when the highest 
degree of evidence is required. 

Sec. VIII 3. Testimony the Ground of Historical 

Knowledge. 
But there are many facts that will not allow of an 
appeal to the senses, and in this case testimony is the 
true and only foundation of our judgments. All hu- 
man actions, of whatever kind, when considered as 
already past, are of the nature here described ; because 



I 



ELEMENTS OF LOGIC. 103 

having now no longer any existence, both the facts 
themselves, and the circumstances attending them, 
can be known only from the relations of such as had 
sufficient opportunities of arriving at the truth. Testi- 
mony, therefore, is justly accounted a third ground of 
human j udgment : and as from the other two we have 
deduced scientifical and natural knowledge, so may we 
from this derive historical; by which I would be un- 
derstood to mean« not merely a knowledge of the civil 
transactions of states and kingdoms, but of all facts 
whatsoever, where testimony is the ultimate founda- 
tion of our belief. 

Sec. IX The second Operation of the Mind, common- 
ly extended beyond Intuition. 

Before I conclude this chapter, it Avill be necessary 
to observe, that though the second operation of the 
mind, properly speaking, extends not bej^ond intuitive 
perceptions, yet logicians have not confined themselves 
to so strict a view of it ; but calling it by the name 
judgment, thereby denote all acts of the mind, where 
only two ideas are compared, without the immediate 
interposition of a third. For when the mind joins or 
separates two ideas, though perhaps this is done in 
consequence of a train of previous reasoning, yet if the 
understanding proceeds upon established notions, with- 
out attending to that train of reasoning, its determi- 
nations are still combined as acts of judgment. Thus, 
That God created the universe, that men are accounta- 
ble for their actions, are frequently mentioned by logi- 
cians, as instances of the mind judging. And yet it is 
apparent, that these judgments are by no means of the 
kind we call intuitive ; nay, that it requires much ex- 
ercise of the reasoning faculty, before a man can trace 
their connexion with the perceptions of that name. I 
could in the same manner easily show, that even our 
judgments of experience and testimony, when pursued 
io their source, derive all their power of persuasion, 
from being linked with intuitive truths. But I shall 
wave this inquiry for the present, as being of a nature 
too subtile for a work of this kind. The remark itself, 
however, was needful, as well to illustrate the proper 



104 ELEMENTS OP LOGIC. 

distinction between the powers of the understanding", 
as tot explain the reason, why in this part of logic, we 
extend the second operation of the mind beyond those 
limits, that in strictness of speech belong to it. Let us 
now proceed to consider a little more particularly the 
nature and variety of these our judgments. 



CHAP. II. 

QT AFFIRMATIVE AND NEGATIVE PROPOSITIONS. 



Sec. I The subject and predicate of a Proposition 

explained. 

While the comparing of our ideas is considered 
merely as an act of the mind, assembling them to- 
gether, and joining or disjoining them according to 
the result of its perceptions, we call it judgment ; but 
when our judgments are put into words, they then bear 
the name of propositions. A proposition, therefore, is a 
sentence expressing some judgment of the mind, where- 
by two or more ideas are affirmed to agree or disagree; 
Now, as our judgments include at least two ideas, one 
of which is affirmed or denied of the other, so must a 
proposition have terms answering to these ideas. The 
idea, of which we affirm or deny, and of course the 
term expressing that idea, is called the subject of the 
proposition. The idea affirmed or denied, as also the 
term answering it, is called the predicate. Thus in the 
proposition, God is omnipotent : God is the subject, it 
being of him that we affirm omnipotence ; and om- 
nipotence is the predicate, because we affirm the idea, 
expressed by that word to belong to God. 

Sec. II The Copula, ^c. 

But as in propositions, ideas are either joined or 
disjoined ; it is not enough to have terms expressing 
those ideas, unless we have also some words to denote 



ELEMENTS OF LOGIC. 105 

their agreement or disagreement. That word in a propo- 
sition, which connects two ideas together, is called the 
copula ; and if a negative particle be annexed, we 
thereby understand, that the ideas are disjoined. The 
substantive -verb is commonl}'' made use of for the co- 
pula, as in the above-mentioned proposition, God is 
omnipotent; where it represents the copula, and signi- 
fies the agreement of the ideas God and omnipotence. 
But if we mean to separate two ideas, then, besides the 
substantive verb, we must also use some particle of ne- 
gation, to express this repugnance. The proposition, 
man is not perfect, may serve as an example of this 
kind, where the notion of perfection, being removed 
from the idea oUnan, the negative particle, not, is in- 
serted after the copula, to signify the disagreement be- 
tween the subject and predicate. 

Sec. Ill Propositions sometimes expressed by a single 

word. 
Every proposition necessarily consists of these three 
parts ; but then it is not alike needful, that they be all 
severally expressed in words ; because the copula is of- 
ten included in the term of the predicate ; as when we 
say, he sits ; which imports the same as he is sitting. 
In the Latin language, a single word has often the force 
of a whole sentence. Thus ambulat is the same, as ille 
est arnbidans ; amo, as ego sum amans ; and so in innu- 
merable other instances ; by which it appears, that we 
are not so much to regard the number of words in a 
sentence, as the ideas they represent, and the manner 
in which they are put together. For whenever two 
ideas are joined or disjoined in an expression, though 
of but a single word, it is evident, that we have a sub- 
ject, predicate, and copula, and of consequence a com- 
plete proposition. 

Sec. IV Affirmative and negative Propositions. 

When the mind joins two ideas, we call it an affirma- 
tive judgment; when it separates them, a negative; 
and as any two ideas compared together, must necessa- 
rily either agree or not agree, it is evident, that all our 
judgments fall under these two divisions. Hence, 



i06 ELEMENTS OF LOGIC. 

likewise, the proposition expressing these judgements,, 
are all either affirmative or negative. An affirmative 
proposition connects the predicate with the subject, as, 
a stone is heavy : a negative proposition separates them, 
as God is not the author of evil. Jlffirmation^ there- 
fore, is the same as joining two ideas together ; and 
this is done by means of the copula. Negation^ on the 
contrary, marks a repugnance between the ideas com- 
pared ; in which case a negative particle must be called 
in, to show that the connexion included in the copula 
does not take place. 

Sec. V When the negative particle serves to disjoin 

ideas. 

And hence we see the reason of the rule commonly 
laid down by logicians, that in all negative proposi- 
tions, the negation ought to ajBfect the copula. For as 
the copula, when placed by itself, between the subject 
and the predicate, manifestly binds them together ; it 
is evident, that in order to render a proposition nega- 
tive, the particle of negation must enter it in such man- 
ner, as to destroy this union. In a word, then only are 
two ideas disjoined in a proposition, when the negative 
particle may be so referred to the copula, as to break the 
affirmation included in it, and undo that connexion it 
would otherwise establish. When we say, for instance, 
no mail is perfect ; take away the negation, and the co- 
pula of itself plainly unites the ideas in the proposition. 
But as this is the very reverse of what was intended, a 
negative mark is added, to show that this union does 
not here take place. The negation, therefore, by de- 
stroying the etfect of the copula, changes the very na- 
ture of the proposition, insomuch that instead of bind- 
ing two ideas together, it denotes their separation. On 
the contrary, in this sentence, the man who departs not 
from an upright behaviour, is beloved of God ; the pre- 
dicate, beloved of God, is evidently affirmed of the sub- 
ject an upright man ; so that notwithstanding the nega- 
tive particle, the proposition is still affirmative. The 
reason is plain ; the negation here affects not the copu- 
la, but making properly a part of the subject, serves, 



ELEMENTS OF LOGIC. 107 

with other terms in the sentence, to form one complex 
idea, of which the predicate, beloved of God, is directly- 
affirmed. This, perhaps, to some may appear a mere 
logical refinement, contrived to justify the scholastic 
rule for distinguishing between affirmative and nega- 
tive propositions. But if it be considered, that this dis- 
tinction is of great importance in reasoning, and can- 
not in many cases be made with certainty, but by mcins 
-of this criterion here given, the reader will see suffici- 
ent reason for my taking so much pains to illustrate it. 

Sec. vi....jF/bt)!; a Copula comes to he a part of a ne- 
gative proposition. 

Perhaps it may still appear a mystery, how a copu- 
la can be said to be a part of a negative proposition, 
whose proper business it is to disjoin ideas. This dif- 
ficulty, however, will vanish, if we call to mind, that 
every judgment implies a direct affirmation, and that 
this affirmation alone makes the true copula in a propo- 
sition. But as our affirmations are of two kinds, viz. ei- 
ther of agreement or of disagreement, between the ideas 
compared ; hence there is also a twofold expression of 
our judgments. In the case of agreement, the copula 
alone suffices ; because it is the proper mark whereby 
we denote an identity or conjunction of ideas. But 
where perceptions disagree, there we must call in a ne- 
gative particle : and this gives us to understand that 
the affirmation implied in the copula, is not of any con- 
nexion between the subject and predicate, but of their 
mutual opposition and repugnance. 



^3::< 



CHAP. III. 

OF UNIVERSAL AND PARTICULAR PROPOSITIONS. 



Sec. I Division of Propositions into Universal and 

Particidar. 
The next considerable division of propositions, is 
into universal and particular. Our ideas, according 



108 ^ ELEMENTS OF LOGIC. 

to what has been already observed in the first part, 
are all singular, as they enter the mind, and repre- 
sent individual objects. But as by abstraction we can 
render them universal, so as to comprehend a whole 
class of things, and sometimes several classes at once ;. 
hence the terms expressing these ideas must be in 
like manner universal. If, therefore, we suppose any 
general term to become the subject of a -proposition, 
it is evident, that whatever is affirmed of the abstract 
idea belonging to that term may be affirmed of all 
the individuals to which that idea extends. Thus when 
we say, men are mortal ; we consider mortality, not as 
confined to one or any number of particular men, 
but as what may be affirmed without restriction of 
the whole species. By this means, the proposition be- 
comes as general as the idea which makes the subject 
of it, and indeed derives its universality entirely from 
that idea> being more or less so, according as this may 
be extended to more or fewer individuals. But it is/ 
further to be observed of these general terms, that they 
sometimes enter a proposition in their full latitude, 
as in the example given above ; and sometimes appear 
with a mark of limitation. In this last case, we are 
given to understand, that the predicate agrees not Xo 
the whole universal idea, but only to a part of it ; 
as in the proposition, some men are wise : for here 
wisdom is not affirmed of every particular man, but 
restrained to a few of the human species. 

Sec. II. ...Propositions universal where the subject is so, 
without a mark of restriction. 

Now from this different appearance of the general 
idea, tljat constitutes the subject of any judgment, ari- 
ses the division of propositions into universal and par- 
ticular. An universal proposition is that, wherein the 
subject is some general term, taken in its full latitude, 
insomuch that the predicate agrees to all the individuals 
comprehended under it, if it denotes a proper species ; 
and to ai! the several species and their individuals, if 
it marks an idea of a higher order. The words, allj 
every f no, jiowe, &c. ar^ the proper signs of this univer- 



E-LEMENTS OF LOGIC. 109 

j>ality ; and as they seldom fail to accompany _^eneral 
truths, so they are the most obvious criterion whereby 
to distinguish them. All animals have a j^ozfoet^ of be- 
ginning motion. This is an universal proposition ; as 
we know from the word all, prefixed to the subject 
animal, which denotes that it must be taken in its 
full extent. Hence the power of beginning motion 
may be affirmed of all the several species of animals ; 
as of birds, quadrupeds, insects, fishes, Lc, and of all 
the individuals of which these different classes consists 
as of this hawk, that horse, and so for others. 

Sec. III. ...Propositions particular U'liere some univer-. 
sal Subjects appear with a Mark oj" Limitation, 

A particular proposition has in like manner some ge- 
neral term for its subject, but with a mark of limita- 
tion added, to denote, that the predicate agrees only to 
some of the individuals comprehended under a species, 
or to one or more of the species belonging to any ge-^ 
nus, and not to the whole universal idea. Thus, sotne 
stones are heavier than iron ; some men have an uncom- 
mo7i share oj" prudence. In the last of these proposi- 
tions, the subject, some men, implies only a certafn 
number of individuals, comprehended under a single 
species. In the former, where the subject is a genus, 
that extends to a great variety of distinct classes, 
some stones may not only imply any number of particu- 
lar stones, but also several whole species of stones ; 
inasmuch as there may be not a few, with the property 
there described. Hence we see, that a proposition does 
not cease to be particular, by the predicrrte's agreeing 
to a whole species, unless that species, singly and dis- 
tinctly considered, makes Mso the subject of which we 
affirm or deny. For if it belongs to some genus, that 
has other species under it, to which tlie predicate does 
not agree ; it is plain, that where this genus is that of 
which we affirm or deny, the predicate agreeing only 
to a part of if, and not to the whole general idea, con- 
stitutes the proposition particular. 
K 



no ELEMENTS OF LOGIC, 

Sec. IV. ...^A sure and infallible Criterion^ whereby to 
distinguish between universal and particular Proposi- 
tions. 

Here, then, we have a sure and infallible mark, 
whereby to distinguish between universal and particu- 
lar propositions. Where the predicate agrees to all the 
individuals comprehended under the notion of the sub- 
ject, there the proposition is universal ; where it be- 
longs only to some of them, or to some of the species 
of the general idea, there the proposition is particular. 
This criterion is of easy application, and much safer 
than to depend upon the common signs of all, every, 
some, none, &c. because these being different in dif- 
ferent languages, and often varying in their significa- 
tion, are very apt in many cases to mislead the judg- 
ment. Thus if we say, all the soldiers when drawn 
Wi formed a square of a hundred men a side : it is evi- 
dent that the predicate cannot be affirmed of the sever- 
al individuals, but of the whole collective idea of the 
subject ; whence, by the rule given above, the proposi- 
tion is not universal. It is true, logicians lay down 
many observations, to enable us to distinguish aright 
on this head : but if the criterion here given be duly 
attended to, it will be of more real service to us than 
an hundred rules. For it is infallible, and may be ap- 
plied with ease ; whereas the directions, which we meet 
with in treatises of logic, being drawn for the most part 
from the analogy of language, and common forms of 
speech, are not only burdensome to the memory, but of- 
ten very doubtful and uncertain in their application. 

Sec. v.. Singidar Propositions contained under the 

head of particulars. 
There is still one species of propositions that remains 
to be described ; and which the more deserves our no- 
tice, as it is not yet agreed among logicians, to which 
of the two classes mentioned above, they ought to be 
referred. I mean singular propositions ; or those where 
the subject is an individual. Of this nature are the fol- 
lowing : sir Isaac Kewion was the inventor ofjiuxions; 
this book contains many useful truths. What occasions 



ELEMENTS OF LOGIC. Ill 

soiie difficulty, as to the proper rank of these proposi- 
tions, is, that the subject being taken according to the 
whole of its extension, they sometimes have the same 
eflfect in reasoning, as universals. But if it be con- 
sidered, that they are, in truth, the most limited kind 
of particular propositions, and that no proposition can, 
with any propriety, be called universal, but where the 
subject is some universal idea ; we shall not be long in 
determining to which class they ought to be referred. 
When we say, some books contain useful truths, the 
proposition is particular ; because the general term ap- 
pears with a mark of restriction. If, therefore, we say, 
this book contains useful truths ; it is evident, that the 
proposition must be still more particular, as the limita- 
tion, implied in the word, tJiis, is of a more confined 
nature, than in the former case. I know, there are in= 
stances, where singular propositions have the same ef- 
fect in reasoning, as universals ; yet is not this, by rea- 
son of any proper universality, belonging to them ; but 
because the conclusion, in such cases being always sin- 
gular, may be proved by a middle term which is also 
singular ; as I could easily demonstrate, were this a pro- 
per place for entering into a discussion of that nature. 

Sec. VI. ...The Fourfold Division of Propositions. 

We see, therefore, that all propositions are either 
affirmative or negative ; nor is it less evident, that in 
both cases, they be universal or particular. Hence 
arises that celebrated fourfold division of them, into 
universal affirmative, and universal negative ; particu- 
lar affirmative, and particular negative ; which com- 
prehends, indeed all their varieties. The use of this- 
method of distinguishing them will appear more fully 
afterwards, when we come to treat of reasoning and 
syllogism. 



iJ2 ELEMENTS OF LOGIC, 



CHAP. IV. 

OF ABSOLtJTE AND CONDITIONAL PROPOSITIONS. 

Sec. I..., Distinction of Qualities into Essential and 
Accidental. 
The objects, about which we are chieflj conver- 
sant in this world, are all of a nature liable to 
t:hang'e. What maybe affirmed of them at one time 
canuot often at another ; and it makes no small part 
of our knowledge to distinguish rightly these varia- 
tions, and trace the reasons upon which thej^ depend. 
For it is observable, that amidst all the vicissitudes of 
nature, some things remain constant and invariable ; 
nor are even the changes to which we see others liable, 
effected, but in consequence of uniform and stead}' 
laws, which, when known, are sufficient to direct us in 
our judgments about them. Hence philosophers, in 
distinguishing the objects of our perception into vari- 
ous classes, have been very careful to note, that some 
properties belong essentially to the general idea, so as 
not to be separable from it but by destroying its very 
nature ; while others are only accidental, and may be 
affirmed or denied of it, in different circumstances. 
Thus, solidity, a yellow colour, and great weight, are 
considered as essential qualities of gold ; but whether 
it shall exist as an uniform, conjoined mass, is not 
alike necessary. We see that by a proper menstruum, 
it may be reduced to a fine powder ; and that inlense 
heat will bring it into a state effusion. 

Sec. II Hence a considerable Diversity in our Man- 
ner of judging. 

Now, from this diversity in the several qualities of 
things, arises a considerable difference as to the man- 
ner of our judging about them. For in this first place, 
all such properties, as are inseparable from objects, 
when considered as belonging to any genus or species, 
are affirmed absolutely and without reserve of that ge» 



ELEMENTS OF LOGIC. I 13 

neral idea. Thus we S3ij ; gold is very 'si^eighty ; a 
stone is hard ; animals have a power of self-motion. 
But in the case of mutable or accidental qualities, as 
they depend upon some other consideration, distinct 
from the general idea ; that also must be taken into the 
account, in order to form an accurate judgment. Should 
we affirm, for instance, of some stones, that they are 
very susceptible of a rolling motion ; the proposition, 
while it remains in- this general form, cannot with any, 
advantage be introduced into our reasonings. An apt- 
ness to receive that mode of motion flows from the fi- 
gure of the stone ; which, as it may vary infinitely, our 
judgment then onh' becomes applicable and determine 
ate, when the particular figure, of which volubility is a 
consequence, is also taken into the account. Let us 
then bring in this other consideration, and the proposi- 
tion will run as' 'ollows : stones of a spherical form arf. 
easily 2}iU into a ^rolling motion. Here we see the con- 
dition upon which the predicate is affirmed, and there- 
fore know in what particular cases the. proposition may 
be applied. 

Sec. III.. ..Which gives rise to the divisioji nf ProjWji- 
tions into Absolute and Coiiditional. 

This consideration of propositions, respecting the 
manner in vrhich the predicate is affirmed of the subject, 
gives rise to the division of them into absolute and*f con- 
ditional. Absolute propositions are those, wherein we 
affirm some property inseparable from the idea of the 
subject, and which, therefore, belongs to it in all possi- 
ble cases ; as, God is infinitely wise :■ virtue tends to the 
ultimate happiness of man. But where the predicate is 
not necessarily, connected with the idea of tlie subject, 
unless upon some consideration distinct from that idea, 
there the proposition-is called conditional. The reason 
of the name is taken from the supposition annexed, 
which is of the nature of a condition, and may be ex- 
pressed as such. Thus ; if a stone is exposed to the rays 
of the sun i it will contract some degree of heat. If a 
river 7'uns in a very declining channel^ its rapiditii .zvill 
'Constantly increase, 

K 2 



114 ELEMENTS OF LOGIG. 

Sec. IV.,.. The great importance of this division, as it 
renders Propositions determinate ; 
There is not any thing of greater importance in phi- 
losophy, than a due attention to this divison of pro- 
positions. If we are careful never to affirm things abso- . 
lutely, but where the ideas are inseparably'- conjoined ; 
and if, in our other judgments, we distinctly mark the 
conditions, which determine the predicate to belong to 
the subject : we shall be the less liable to mistake, in 
applying general truths to the particular concerns of 
human life. It is owing to the exact observance of 
this rule, that mathematicians have been so happy in 
their discoveries; and that what they demonstrate of 
magnitude in general, maybe applied with ease in all 
obvious occurrences. 

Sec. V And reduces them from particulars to ge- 
nerals. 

The truth of it is, particular propositions are then 
known to be true, when we can trace their connexion 
with universals : and it is, accordingly, the great busi- 
ness of science, to find out general truths, that may be 
applied with safety in all obvious instances. Now the 
great advantage arising from determining with care 
the conditions upon which one idea may be affirmed or 
denied of another, is this ; that thereby particular pro- 
positions really become universal, may be introduced 
with certainty into our reasonings, and serve as stand- 
ards to conduct and regulate our judgments. To illus- 
trate this by a familiar instance : if we say, some wa- 
ter acts very forcibly ; the proposition is particular: 
and as the conditions, on which this forcible action 
depends, are not mentioned, it is as yet uncertain in 
what cases it may be applied. Let us then supply these 
conditions, and the proposition will run thus ; water 
conveyed in sufficient quantity along a steep^ descent, 
acts very forcibly. Here we have an universal judg- 
ment, inasmuch as the predicate, forcible action, may 
be ascribed to all water under the circumstances men- 
tioned. Nor is it less evident, that the proposition in 
this new form is of easy application : and in fact we 



ELEMENTS OP LOGIC. 115 

find, that men do apply it in instances where the for- 
cible action of water is required ; as in corn mills, and 
many other works of art. ^ hus we see, in what man- 
ner we are to proceed, in ordei- io arrive at universal 
truths, which is the great end and aim of science. 
And indeed, would men take the same care, duly to 
express the conditions on which they affirm and deny, 
as mathematicians do, in those theorems which they 
term hypothetical, I doubt not, but we might be able 
to deduce many truths, in other parts of philosophy, 
with no less clearness, force, and perspicuity, than has 
hitherto been thought peculiar to the science of quantity. 



■=:a::< 



CHAP, V. 

OF SIMPLE AND COMPOUND PROPOSITIONS. 

Sec. I..., Division of Propositions into Simple and 
Compound* 
Hitherto we have treated of propositions, where 
only two ideas are compared together. These are 
in the general, called siwi;3/e : because, having but one 
subject and one predicate, they are the effect of a 
simple judgment that admits of no subdivision. But 
if it so happens, that several ideas offer themselves 
to our tlioughts at once whereby we are led to affirm 
the same thing of different objects, or different things 
of the same object ; the propositions, expressing 
these judgments, are called compound; because they 
may be resolved into as many others as there are 
subjects or predicates in the whole complex determina- 
tion of the mind. Thus, Goc? is infinitely 'wise and in- 
finitely powerful ; here there are two predicates, in- 
finite wisdom and infinite power, both affirmed of the 
same subject ; and accordingly, the proposition may 
be resolved into two others, affirming these predicates 
severally. In like manner, in the proposition, neither 
kings nor people are exempt from death, the predicate 
is denied of both subjects, and may therefore be sepa- 



116 ELEMENTS OF LOGIC. 

rated from them, in distin-ct propositions. Nor is it 
less evident, that if a complex judgment consists of 
several subjects and predicates, it may be resolved into 
as many simple propositions as are the number of dif- 
ferent ideas compared together. Riches and honours 
are apt to elate the mind, and increase the number of 
our desires. In this judgment, there are two subjects 
and two predicates : and it is at the same time apparent, 
that it may be resolved into four distinct propositions. 
Riches are apt to elate the mind . Riches are apt to 
increase the number of our desires. And so of honours. 

Sec. II.... The proper Notion of a Compound Proposi- 
tion, ascertained. _^ 

Logicians have divided these compound propositions 
into a great many different classes ; but in my opi- 
nion, not with a due regard to their proper definition. 
Thus conditionals, casuals, relatives, ^"c. are mention- 
ed as so many distinct species of this kind, though m 
fact they are no more than simple propositions. To 
give an instance of a conditional : If a stone is expos- 
ed to the rays of the sun, it will contract some degree of 
heat. Here we have but one subject and one predi- 
cate ; for the complex exTpiession, A stone exposed to 
the rays of the sun, constitutes the proper subject of 
this proposition, and is no more than one determinate 
idea. The same thing happens in casuals. Rehoboam 
was unhappy, because he followed evil counsel. I deny 
not, that there is here an appearance of two proposi- 
tions arising from the complexity of the expression ; 
but when we come to consider , the matter more near- 
ly, it is evident that v/e have but a single subject and 
predicate....T/ie pursuit of evil counsel brought misery 
upon Rehoboam. It is not enough, therefare, to ren- 
der a proposition compound, that the subject and pre- 
dicate are complex notions, requiring sometimes a whole 
sentence to express them ; for in this case, the com- 
parison is still confined to two ideas, and constitutes 
what we call a simple judgment. But where there are 
several subjects or predicates, or both, as the affirma- 
tion or negation may be alike extended to them all, the 
■proposition; expressing such a judgment, is truly a col- 



ELEMENTS OF LOGIC. 117 

Jection of as many simple ones, as there are different 
ideas compared. Confining ourselves, therefore, to 
this more strict and just notion of compound proposi- 
tions, they are all reducible to two kinds, viz. copula- 
tives and disjunctives. 

Sec. III.... Compound Propositions either Copulative, 
A copulative proposition is, where the subjects and 
predicates are so linked together, that they may be all 
severally affirmed or denied one of another. Of this na- 
ture are the examples of compound propositions given 
above. Riches and honours are apt to elate the mind^ and 
increase the number of our desires. Neither kings nor 
people are exempt from death. In the first of these, 
the two predicates may be affirmed severally of each 
subject, whence we have four distinct propositions. 
The other furnishes an example of the negative kind, 
where the same predicate being disjoined from both 
subjects, may be also denied of them in separate pro- 
positions. 

Sec. IV ... .Or Disjunctive. 
The other species of compound propositions are those 
called disjunctives ; in which, comparing several pre- 
dicates with the same subject, we affirm, that one of 
them necessarily belongs to it, but leave the particular 
predicate undetermined. If any one, for example, 
says : This "world either exists of itself or is the work 
of some all-wise and powerful cause ; it is evident, that 
one of the two predicates must belong to the world ; 
but as the proposition determines not which, it is 
therefore of the kind we call disjunctive. Such, too, 
are the following : The sun either moves round, the 
earth, or is the centre about which the earth revolves. 
Friendship finds men equal or makes them so. It is the 
nature of all propositions of this class, supposing them 
to be exact in point of fonn, that upon determining the 
particular predicate, the rest are of course to be re- 
moved ; or if all the predicates but one are removed ; 
that one necessarily takes place. Thus, in the exam- 
ple above, if we allow the world to be the work of some 
wise and powerful cause, we of course deny it to be 



118 ELEMENTS OP LOGIC. 

self-existent ; or if we deny it to be self-existent, we 
must necessarily admit that it was produced by some wise 
and powerful cause. Now this particular manner of 
linking the predicates together, so that the establishing 
one displaces all the rest. ...or the excluding all but one 
necessarily establishes that one.. ..cannot otherwise be 
effected than by means of disjunctive particles. And 
hence it is, that propositions of this class take their 
names from these particles, which make so necessary a 
part of them, and indeed, constitute their very nature, 
considered as a distinct species. But I shall reserve 
what farther might be said on this head, till I come to 
treat of reasoning, where the great use and importance 
of disjunctive propositions will better appear. 



CHAP. VI. 

OP THE DITISION OF PROPOSITIONS INTO SELF-EVI- 
DENT AND DEMONSTRABLE. 



Sec. I Design of this Chapter. 

As we are soon to enter upon the third part of lo- 
gic, which treats of reasoning — and as the art of 
reasoning lies in deducing propositions whose truth 
does not immediately appear, from others more known 
— it will be proper, before we proceed any farther, to 
examine a little the diflferent degrees of evidence that 
accompany our judgments ; that we may be the better 
able to distinguish in what cases we ought to have re- 
course to reasoning, and what those propositions are, 
upon which, as a sure and unerring foundation, we may 
venture to build the truth of others. 

Sec. II Pi'opositions divided into Self-evident and 

Demonstrable. 
When any proposition is offered to the view- of the 
mind, if the terms, in which it is expressed, are under- 
stood ; upon comparing the ideas together, the agree- 
ment or disagreement asserted is either immediately per- 
ceived, or found to lie beyond the present reach of the 
iinderstanding. In the first case, the proposition is said 



ELEMENTS OF LOGIC. 119 

to be self-evident f and admits not of any proof; because 
a bare attention to ihe ideas themselves produces full 
conviction and certainty ; nor is it possible to call in 
any thing more evident by way of confirmation. But 
where the connexion or repugnance comes not so readi- 
ly under the inspection of the mind, there we must have 
recourse to reasoning ; and if by a clear series of proofs 
we can make out the truth proposed, insomuch that self- 
evidence shall accompany every step of the procedure, 
we are then able to demonstrate what we assert ; and 
the proposition itself is said to be demonstrable. When 
we atfirm, for instance, that it is impossible for the same 
thing to be and not to be ; whoever understands the 
terms made use of, perceives at first glance the truth of 
what is asserted ; nor can he by srny efforts, bring him- 
self to believe the contrary. The proposition therefore 
is self-evident^ and such that it is impossible by reason- 
ing to make it plainer ; because there is no truth more 
obvious, or better known from which as a consequence 
it may be deduced. But if we say this world had, a be- 
ginning ; the assertion is indeed equally true, but shines 
not forth with the same degree of evidence. We find 
great difficulty in conceiving how the world could be 
made out of nothing ; and are not brought to a free 
and full consent, until by reasoning we arrive at a clear 
view of the absurdity involved in the contrary supposi- 
tion. Hence this proposition is of the kind we call 
demonstrable^ inasmuch as its truth is not immediately 
perceived by the mind, but yet may be made appear by 
means of others more known and obvious, whence it 
follows as an unavoidable consequence. 

Sec III. ...Why the' second operation of the Mind is 
, corjined "wholly to Intuition, 

From what has been said, it appears that reasoning 
is employed only about demonstrable propositions, and 
that our intuitive and self-evident perceptions are the 
ultimate foundation on which it rests. And now we 
see clearly the reason, why in the distinction of the 
powers of the understanding, as explained in the in- 
troduction to the treatise, the second operation of the 



120 ELEMENTS OF LOGIC. 

mind was confined wholly to intuitive acts. Our first 
step in the way to knowledge, is to furnish ourselves 
with ideas. When these are obtained, we next set our- 
selves to compare them together, in order to judge of 
their agreement or disagreement. If the relation we 
are in quest of, lie immediately open to the view of the 
mind, the judgments expressing them are self-evident ; 
and the act of the mind, forming these judgments, is 
what we call intuition. But if, upon comparing our 
ideas together, we cannot readily and at once trace 
their relation, it then becomes necessary to employ 
search and examination, and call in the assistance of 
self-evident truths, which is what we properly term 
reasoning. Every judgment, therefore, that is not in- 
tuitive, being gained by an exercise of the reasoning 
faculty, necessarily belongs to the third operation of 
the mind, and ought to be referred to it in a just divi- 
sion of the powers of the understanding. And indeed 
it is with this view chiefly, that we have distinguished 
propositions into self-evident and demonstrable. Un- 
der the first head are comprehended all our intuitive 
judgments, that is, all belonged to the second opera- 
tion of the mind. Demonstrable propositions are the 
proper province of the reasoning faculty, and consti- 
tute by far the most considerable part of human know- 
ledge. Indeed reason extends also to matters of expe- 
rience and testimony, where the proofs adduced are not 
of the kind called demonstration. But I am here only 
considering the powers of the mind as employed in tra- 
cing the relations between its own ideas, in which 
view of things, every true proposition is demonstrable ; 
though very often we find ourselves incapable of disco- 
vering and applying those intermediate ideas upon 
which the demonstration depends. 

Sec. ly.... Self -evident Truths the first principles of 
Reasoning. 

Demonstrable propositions, there fore, belonging pro- 
perly to the third operation of the mind, I shall, for 
the present, dismiss them, and return to the consider- 
ation of self-evident truths. These as I have already 



ELEMENTS OF LOGIC. 121 

observed, furnish the first principles of reasoning ; and 
it is certain, that if in our researches, we employ only 
such principles as have this character of self-evidence, 
and apply them according to the rules to be after- 
wards explained, we shall bq in no danger of error, in 
advancing from one discoveiy to another. For this I 
may appeal to the writings of the mathematicians, 
which, being conducted by the express model here 
mentioned, are an incontestibk proof of the firmness 
and stability of human knowledge, when built upon so 
sure a foundation. For not only have the propositions 
of this science stood the test of ages, but are found 
attended with such invincible evidence, as forces the 
assent of all who duly consider the proofs upon' which 
they are established. Since then mathematicians are 
universally allowed to have hit upon the right method 
of arriving at truths — since they have been the happiest 
in the choice, as well as application of their principles 
— it may not be amiss to explain here the divisions they 
have given of self-evident propositions ; that, by tread- 
ing in their steps, we may learn something of that just- 
ness and solidity of reasoning, for which they are so de- 
servedly esteemed. 

Sec. v.... Definitions a great help to Clearness and Evi- 
dence in Knowledge. 

First, then it is to be observed, that they have been 
very careful in ascertaining their ideas, and fixing the 
significations of their terms. For this purpose they 
begin with definitions, in which the meaning of their 
words is so distinctly explained, that they cannot fail 
to excite in the mind of an attentive reader the very 
same ideas as are annexed to them by the writer. And 
indeed I am apt to think that the clearness and irre- 
sistible evidence of mathematical knowledge, is owing 
to nothing so much as this care in laying the founda- 
tion. Where the relation between any two ideas is 
accurately and justly traced, it will not be difficult for 
another to comprehend that relation, if in setting him- 
self to discover it, he brings the very same ideas into 
comparison. But if, on the contrary, he affixes to his 
L 



122 ELEMENTS OF LaftlC. 

Words ideas cliffe rent from those that were in the mind 
ef him who first advanced the demonstration ; it is evi- 
dent, that as the same ideas are not compared, the same 
relation cannot subsist, insomuch that a proposition 
will be rejected as false, which had the terms been 
rightly understood must have appeared unexceptiona- 
bly true. A square, for instance, is a figure bounded 
by four equal right lines, joined together at right an- 
gles. Here the nature of the angles make no less ^ 
part of the idea, than the equality of the sides ; and 
many properties, demonstrated of the square, flow from 
its being a rectangular figure. If, therefore, we sup- 
pose a man who has formed a partial notion of a square* 
comprehending only the quality of its sides, without 
regard to the angles, reading some demonstration that 
implies also' this latter consideration; it is plain he 
would reject it as not universally true, inasmuch as it 
could not be applied where the sides were joined to- 
gether at unequal angles. For this last figure, answer- 
ing still to his idea of a square, would be yet found 
without the property assigned to it in the proposition, 
but if he comes afterwards to correct his notion, and 
render his idea complete, he will then readily own the 
truth and justness of the demonstration. 

Sec. VI.... Mathematicians by beginning with them, pro-' 
cure a ready reception to the truths they advance. 

We see, therefore, that nothing contributes so muck 
^to the improvement and certainty of human know- 
ledge, as the having determinate ideas, and keeping 
them steady and invariable in all our discourses and 
reasonings about them. And on this account it is, that 
mathematicians, as was before observed, always begin 
by defining their terms, and distinctly unfolding the 
notions they are intended to express. Hence such as 
apply themselves to these studies, having exactly the 
same views of things, and bringing always the very 
same ideas into comparison, readily discern the rela- 
tions between them, when clearly and distinctly repre- 
-sented. Nor is there any more natural and obvious 
iireasou for the universal reception given to mathemati- 



ELEMENTS OP LOGIC. 12S 

<Sal truths, and for that harmony and correspondence 
of sentiments which makes the distinguishing charac* 
ter of the literati of this class. 

Sec. vii....T/*e establishing of Principles the Second 
Step in Mathematical Knowledge. 
When they have taken this first step, and made 
known the ideas, whose relations they intend to inves- 
tigate, their next care is, to lay down some self evi- 
dent truths, which may serve as a foundation for 
their future reasonings. And here, indeed, they pro- 
ceed with remarkable circumspection, admitting no- 
principles but what flow immediately from their defini- 
tions, and necessarily' force themselves upon a mind in 
any degree attentive to its perceptions. Thus a cir- 
cle is a figure formed by a right line, moving round 
some fixed point in the same plane. The fixed point, 
round which the line is supposed to move, a«d where 
one of its extremities terminates, is called the centre 
of the circle. The other extremity', which is conceiv- 
ed to be carried round, until it returns to the point 
whence it first set out, describes a curve running into 
itself, and termed the circumference. All right lines, 
drawn from the centre to the circumference, are called 
radii. From these definitions compared, geometri- 
cians derive this self-evident truth, that the radii of the 
same circle are all equal one to another. I call it self- 
evident, because nothing more is required, to lay it 
open to the immediate perception of the mind, than an 
attention to the ideas compared. For from the very 
nature of a circle it is plain, that the circumference is 
every where distant from the centre, by the exact 
length of the describing line; and that the several ra- 
dii are in truth nothing more, than one and the same 
line variously posited within the figure. This short 
description will, I hope, serve to give some little in-- 
sight into the manner of deducing mathematical prin- 
ciples, as well as into the nature of that evidence 
which accompanies them. 

Sec. will. ...Propositions divided into Speculative and 
Practical. 
And now I proceed to observe, that in all proposi- 



124 ELEMENTS OF LOGIC. 

tions we either affirm or deny some property of the 
idea that constitutes the subject of our judgment, or 
we maintain that something may be done or effected. 
The first sort is called speculative propositions, as in 
the example mentioned above, the rodii of the same 
circle are all equal one to another. The others are cal- 
led practical^ for a reason too obvious to be mention- 
ed; thus, that a right line maybe drawn from one 
point to another, is a practical proposition ; inasmuch 
as it expresses that something may be done. 

Sec. IX. ...Hence Mathematical Principles distinguish- 
ed into Axioms and Postulates. * 

From this twofold consideration of propositions, ari- 
ses the twofold division of mathematical principles, 
into axioms and postulates. By an axiom they under- 
stand any self-evident speculative truth : as, that the 
whole is greater than its parts : that things equal to 
one and the same thing, are equal to another. But 
a gelf-ev^ident practical proposition is what they call a 
postulate. Such are these Q>i Euclid ; that ajinite right 
line may be continued directly Jorzuards : that a circle 
may be described about any centre with any distance. 
And hej:e we are to observe, that ns in an axiom, the 
agreement or disagreement between the subject and 
predicate, must come under the immediate inspection 
of the mind ; so in a posiidate, not only the possibility 
of the thing asserted must be evident at first view, but 
also the manner in which it may be eft'ected. But 
where this manner is not of itself apparent, the propo- 
sition comes under the notion of the demonstrable kind, 
and is treated as such by the geometrical writers. 
Thus, to draw a line from one point to another, is as- 
sumed by Euclid as di postulate, because the manner of 
doing it is so obvious, as to require no previous teach- 
ing. But then it is not equally evident, how we are 
to construct an equilateral triangle. For this reason he 
advances it as a demonstrable proposition, lays down 
rules for the exact performance, and at the same time 
proves, that if these rules are followed, the figure will 
be justly described. 



ELEMENTS OP LOGIC. V25 

Sec. x....And demonstrabh Propositions into Theo- 
rems and Problems. 
This natura'ly leads me to tales notice, that as self- 
evideit truths dive distinguished into different kinds, ac- 
cording" as they are specuh.tive or practical ; so is it al- 
so with c?e;no7isfra6?e propositions. A demonstrable spe- 
culative proposition is by mathematicians called a theo- 
rem. Such is the famous 47th proposition of the first 
book of the elements^ known by -the name of the Pytha- 
goric theorem, from its supposed inventor, Pythagoras ^ 
viz. That in every right-angled triangle^ the square des- 
cribed upon the side subtending the right angle^ is equal 
to both the squares described wpon the sides containing 
the right angle. On the other hand, a demonstrable prac- 
tical proposition is called a j^roo/cm ; as where Euclid- 
teaches us to describe a square upon a given right line. 

Sec. XI.... Corollaries are obvious deductions from The- 
orems or Problems. 
Since I am upon this subject, it may not be amiss to 
add, that besides the four kinds of propositions already 
mentioned, mathematicians have also a fifth, known by 
the name of corollaries. These are usually subjoined to 
theorems or problems^ and differ from them only in this, 
that they flow from what is there demonstrated, in so- 
obvious a manner as to discover their dependence upon 
the proposition whence they are deduced, almost as soon 
as proposed. Thus Euclid haiving demonstidited, that in 
every right-lined triangle, all the three angles taken toge- 
ther are equal to two right angles ; adds, by way of co- 
rollary, that all the three angles of any one triangle taken 
together, are equal to all the three angles of any other 
triangle, taken together : which is evident at first sight ; 
because in all cases they are equal to tivo right ones, 
and things equal to two and the same things, are equal 
to one another. 

Sec. xn....Scolia serves the purposes of Annotation 

or a comment. 

The last thing I shall take notice of, in the practice 

of the mathematicians, is what they Call their scholiaj , 

They are indifferently aanexed to definitions, proposi- 



.HS ELEMENTS OF LOGIC- 

tons, or corollaries ; and answer the same purposes ai 
annotations upon a classic author.- For in them occasion 
is taken, to explain ^vhatever may appear intricate and 
obscure in a train of reasoning ; to answer objections ; 
to teach the application and uses of propositions ; to 
lay open the original and history of the several disco- 
veries made in the science ;. and in a word, to acquaint 
us with ail such particulars as deserve to be known, 
whether considered as points of curiosity or profit. 
Sec. xui,.,,.Th2S method of the Mathematicians 
universal, and a sute guide to Certainty. 
Thus we have taken a short view of the so much 
celebrated method of the mathematicians; which, \o 
any one who considers it with a proper attention, must 
needs appear universal, and equally applicable in other 
sciences. They begin with definitions. From these 
they deduce their axioms and postulates, which serve 
as principles of reasoning ; and having thus laid a firm 
ioundation, advance to theorems and problem.s, es= 
tablishing all by the strictest rules of demonstration. 
The corollaries flow naturally and of themselves. And if 
any particulars are. still wanting to illustrate a subject, 
or complete the reader's information ; these, that tha 
series of reasoning may not be> interrupted or broken, 
are generally thrown , into scolia^ In. a svstem of 
knowledge so uniform and well connected, no wonder 
if we meet, with certainty; and if those clouds and 
darknesses, that deface other parts of human science 
and bring discredit even upon reason itself, are her^> 
scattered and disappear. 

Sec XIV. >,.. Self-evident Truths known- hi/ the appa^ 
rent unavoidable Connexion between the Subject and 
Predicate,, 

But I shall for the present wave these reflections, 
which every reader of understanding is able to make 
of himself, and return to the consideration of. self-evi-J. 
dent propositions. It will, doubtless, be expected, af° 
ter what has been here said of them,, that I should 
establish some criteria, or marks, by which they may- 
be di-linguished, Byl I frankly own my inability m 



ELEMENTS OF LOGIC. 127 

this respect, as not being able to conceive any thing in. 
them mere obvious and striking, than that self-evidence 
which constitutes their very nature. All I have there- 
fore to observe on this head, is, that we ought to make 
it our first care, to obtain clear and determinate ideas. 
When afterwards we come to compare these together, 
if we perceive between any of them a necessary and 
unavoidable connexion, insomuch that it is impossible 
to conceive them existing asunder, without destroying 
the very ideas compared ; we may then conclude, that 
the proposition expressing this relation is a principle, 
and of the kind we call self-evident. In the example 
mentioned above, the radii of the same circle arc all 
equal between themselves, this intuitive evidence shines 
forth in the clearest manner ; it being impossible for 
any one, who attends his own ideas, not to perceive the 
equality here asserted. For as the circumference is 
every where distant from the centre by the exact 
l'?ngth of the describing line ; the radii drawn from 
tae centre of the circumference, being severally equal 
to this one line, must needs also be equal among them- 
selves. If we suppose the radii unequ^il, we at the same 
time suppose the circumference more distant from the 
centre in some places than in others ; from which sup- 
position, as it would exhibit a figure quite different 
from a circle, we see there is no separating the predir 
cate from the subject in the proposition, without de- 
stroying the idea in relation to which the comparison 
was made. The same thing will be found to hold in 
all our other intuitive perceptions, insomuch that we 
may establish this as an universal criterion, whereby 
to judge of, and distinguish them. I would not, how- 
ever, be'understood to mean, as if this ready view of 
the unavoidable connexion between some ideas was 
any thing really different from self-evidence. It is, 
indeed, nothing more than the notion of self-evidence 
a little unfolded, and as it were laid open to the inspec- 
tion of the mind.. Intuitive judgments need no other 
distinguishing marks, than that brightness which sur- 
rounds them ; in like manner as ligh't discovers itself 
by its own presence,- and the splendor it universally 



J28 ELEMENTS OF LOGIC, 

diffuses. But I have said enough of self-evident pro- 
positions, and shall therefore now proceed to those of 
the demonstrable kind ; which, being gained in conse- 
quence of reasoning, naturally leads us to the third 
part of logic, where this operation of the understanding 
Is explained. 



BOOK iir. 

Of Reasoning. 



CHAP. I. 

#* REASONING IN GENERAL, AND THE PARTS ©F 
WHICH IT CONSISTS. 



Sec. I.,, ^Remote Relations discovered hy means of in- 
termediate Ideas* 

We have seen how the mind proceeds in furnish- 
ing itself with ideas, and framing intuitive per- 
ceptions. Let us next inquire into the manner of 
discovering those more remote relations, which, Ijing 
at a distance from the understanding, are not to be 
traced but by means of a higher exercise of its powers. . 
It often happens in comparing ideas together, that 
their agreement or disagreement cannot be discerned> 
at first view, especially if they are of such a nature, as 
not to admit of an exact application one to another^ 
When, for instance, we compare two figures of a dif- 
ferent noake, in order to judge of their equality or in- 
equality, it is plain, that by barely considering the fi=- 



ilLEMENTS OF L061€. 129 

g.urfes themselves, we cannot arrive at an exact deter- 
mination ; because, by reason of their disagreeing 
forms, it is impossible so to put them together, as that 
their several parts shall mutually coincide. Here then 
it becomes necessary to look out for some third idea, 
that will admit of such an application as the present 
case requires ; wherein if we succeed, all difficulties 
vanish, and the relation we are in quest of may be 
traced with ease. Thus right-lined figures are all re- 
ducible to squares, by means of which we can measure 
their areas, and determine exactly their agreement or 
disagreement in point of magnitude. 

Sec. u...Trhis manner of arriving at Truth and termed 
Reasoning. 

If nov/ it be asked, how any third idea can serve to 
discover a relation between two others ; I answer, 
by being compared severally with these others ; for 
such a comparison enables us to see how far the ideas, 
with which this third is compared, are connected or 
disjoined between themselves. In the example men- 
tioned above, of two right-lined figures, if we com- 
pare each of them with some square whose area is 
known, and find the one exactly equal to it, and the 
other less by a square-inch greater than that of the se- 
cond. This manner of determining the relation be- 
tween any two ideas, by the invention of some third 
with which they may be compared, is that which we 
call reasonings and indeed the chief instrument, by 
which we push on our discoveries, and enlarge cuf 
knowledge. The great art lies, in finding out such in- 
termediate ideas, as, when compared with the others 
in the question, will furnish evident and known truths ; 
because, as will afterwards appear, it is only by means 
of them, that we arrive at the knowledge of what is 
hidden and remote. 

Sec. III.... The parts that constitute an Act of Reasoning 
and a Syllogistn. 

From what has been said, it appears that every act 
of reasoning necessarily includes three disiinct judg- 
ments ; two, wherein the ideas^^ whose relation we 



130 ELEMENTS OF LOGIC. 

want to discover, are severally compared with the mid- 
dle idea, and a third, wherein they are themselves con- 
nected op.disjoined according to the result of that com- 
parison. Now as in the second part of logic, our judg- 
ments when put into words, were called propositions.... 
so here, in the third part, the expressions of our reason- 
ings are termed syllogisms. And hence it follows, that 
as every act of reasoning implies three several judg- 
ments, so every syllogism must include three distinct 
propositions. When a reasoning is thus put into words, 
and appears in a form of a syllogism, the intermediate 
idea, made use of to discover the agreement or disa- 
greement^ we search for, is called the middle term ; and 
the two ideas themselves, with which this third is com- 
pared, go by the name of the extremes* 

Sec. iv....Insta7icei Man and Accountahleness, 

But as these things are best illustrated by examples; 
let us, for instance, set ourselves to inquire, whether 
men are accountable for their actions. As the relation 
between the ideas of man and accountableness comes 
Bot within the immediate view of the mind, our first 
care must be, to find out some third idea, that will ena- 
ble us the more easily to discover and trace it. A very 
small measure of reflexion is sufficient to inform us, 
that no creature can be accountable for his actions, un- 
less we suppose him capable of distinguishing the good 
from the bad : that is unless we suppose him possessed 
df reason. Nor is this alone sufficient. For what 
would it avail him, to know good from bad actions, if he 
had no freedom of choice, nor could avoid the one, and 
pursue the other ? Hence it becomes necessary to take 
in both considerations in the present case. It is at the 
same time equally apparent, that wherever there is this 
ability of distinguishing good from bad actions, and pur- 
suing the one and avoiding the other, there also a crea- 
ture is accountable. We have then got a third idea, 
with which accountableness is inseparably connected, t;i2', 
reason and liberty ; which are here to be considered as 
making up one complex conception. Let us now take 
•this middle idea,^ and compare it with the other term te 



ELEMENTS OF LOGIC* 131 

the question, viz. man, and we all know by experience 
that It ■> >y be affirmed of him. Having- thus, by means 
of the inteirmediate idea, formed two several judgments, 
viz. that liKAii is possessed of reason and liberty ; and that 
^reason and liberty imply ac count ableness; a third obvious- 
ly and necessarily ff»liuws, viz. that man, is accountable 
for his actions. Here then we have a complete act of rea- 
soning, in which, according to what has been already 
observed, there are three distinct judgments ; two that 
maybe styled previous, inasmuch as tliey lead to the 
other, and arise from comparing the middle idea with 
the two ideas in the question ; the third is a consequence 
of these previous acts, and flows from combining the ex- 
treme ideas between themselves. If now we put this 
reasoning into words, it exhibits what logicians term a 
.syllogism, and, when proposed in due form, runs thus : 

Every creature possessed of reason and liberty is accountable for his ac- 
tions. 
Man is a creature possessed of reason and liberty. 
Therefore man is accountable for his actions. 

Sec. v.... Premises y conclusions^ extremes, middle term, 

In this syllogism we may observe, that there are three 
several propositions, expressing the three judgments 
implied in the act of reasoning, and so disposed as to 
represent distinctly what passes within the mind, in 
tracing the more distant relations of its ideas. The two 
first. propositions answer the two previous judgments in 
reasoning, and are called the premises, because they 
are placed before the other. The third is termed the 
conclusion, as being gained in consequence of what was 
asserted in the premises. We are also to remember, 
that the terms expressing the two ideas whose relation 
we inquire after, as here man and accountableness, are ia 
general, called the ex?!remes ; and that the intermediate 
idea, by means of which, the relation is traced, viz. a 
creature possessed of reason «7icZ/i6erfi/, takes the name 
of the middle term. Hence it follows, that by the pre- 
tnises of a syllogism, we are always to understand the 
two propositions, where the. middle term is severally 
compared with extremes ; for these constitute the pre- 
vious judgments, whence the truth we are in quest of 



132 ELEMENTS OF LOGir. 

is by reasoning deduced. The conclusion is that other 
propositions, in which the extremes themselves are 
joined or separated, agreeably to what appears upon the 
above comparison. All this is evidently seen in the 
foregoing syllogism, where the two first propositions, 
which represent the premises, and the third, which 
makes the conclusion, are exactly agreeable to the defi- 
nitions here given. 

Sec. VI. ...Major and Minor Ternii Major and Minor 
Proposition. 
Before we take leave of this article, it will be far- 
ther necessary to observe, that as the conclusion is 
made up of the extreme terms of the syllogism ; so 
that extreme which serves as the predicate of the con- 
clusion, goes by the name of the major term: the 
other extreme, which makes the subject in the same 
proposition, is called the minor term. From this dis- 
tinction of the extremes, arises also a distinction be- 
tween the premises, where these extremes are several- 
ly compared with the middle term. That proposition, 
which compares the greater extreme, or the predicate 
•f the conclusion, with the middle term is called the 
major proposition : the other, wherein the same mid- 
dle term is compared with the subject of the conclu- 
sion, or lesser extreme, is called the minor proposition. 
All this is obvious from the syllogism already given, 
where the conclusion is, man is accountable for his ac- 
tions. For here the predicate, accountable for his ac- 
tions, being connected with the middle term in the first 
of the two premises. Every creature possessed of rea- 
son and liberty is accountable for his actions, gives what 
we call the major proposition. In the second of the pr'e- 
mises, man is a creature possessed of reason and liberty, 
we find the lesser extreme, or subject, of the conclu- 
sion, viz. man, connected with the same middle term , 
whence it is known to be the minor pro2yosition. I shall 
only add, that when a syllogism is proposed in due 
form, the major proposition is always placed first, the 
minor next, and the conclusion last, according as we 
have done in that offered above. 



ELEMENTS OF LOGIC. 133 

Sec. V II.... Judgment and Proposition^ Reasoning 
and Syllogism distinguished. 
Having thus cleared the way, by explaining such 
terms, as we are likely to have occasion for in the pro- 
gress of this treatise ; it may not be amiss to observe, 
that tho' we have carefully distinguished between the 
act of reasoning, and a syllogism, which is no more 
than the expression of it, yet common language is not 
so critical on this head ; the term reasoning being 
promiscuously used, to signify either the judgments 
of the mind, as they follow one another in train, 
or the propositions expressing these judgments. 
Nor need we wonder that it is so, inasmuch as our 
ideas, and the terms appropriated to them, are so con- 
nected by habit and use, that our thoughts fall as it 
were spontaneously into language, as fast as they 
arise in the mind ; so that even in our reasonings 
within ourselves, we are not able wholly to lay aside 
words. But notwithstanding this strict connexion be- 
tween mental and verbal reasoning, if I may be allow- 
ed that expression, I thought it needful here to dis- 
tinguish them, in order to give a just idea of the man- 
ner of deducing one truth from another. While the 
mind keeps the ideas of things in view, and combines 
its judgments according to the real evidence attending 
them, there is no great danger of mistake in our rea- 
sonings ; because we carry our conclusions no farther 
than the clearness of our perceptions warrants us. 
But whetre we make use of words, the case is oftea 
otherwise ; nothing being more common, than to let 
them pass without attending to the ideas they repre- 
sent ; insomuch that we frequentl}'' combine expres- 
sions, which upon examination appear to have no de- 
terminate meaning. Hence it greatly imports us o 
distinguish between reasoning and syllogism ; and to 
take care, that the one be in all cases the tiue and just 
representation of the other. However, as I am un- 
willing to recede too far from the common forms of 
speech, or to multiply distinctions without necessity, I 
shall henceforward consider propositions as representing"' 
the real judgments of the mind, and syllogisms as th« 
M 



134 ELEMENTS OF LOGIC. 

true copies of our reasonings ; which indeed they ou^ht 
^always to be, and undoubtedly always will be, to men 
who think justly, and are desirous of arriving at truth. 
Upon this supposition there will be no danger U\ using 
the words judgment and proposition promiscuously ; or 
'in considering reasoning as either a combination of va- 
rious judgments, or of the propositions expressing them ; 
because, being the exact copies one of another, the re- 
sult will be in all cases the same. Nor is it a sm?.ll ad- 
vantage, that we can thus conform to common speech, 
without confounding our ideas, or running into ambi- 
guity. By this means we bring ourselves upon a level 
with other men, readily apprehend the meaning of their 
expressions, and can with ease convey our own notions 
and sentiments into their minds. 

Sec. VIII. .../?i a single Act of Reasoning, the Premi- 
ses must be intuitive Truths. 

These things premised, we may in the general define 
reasoning to be an act or operation of the mind, dedu- 
cing some unknown proposition, from other previous ones 
that are evident and known. These previous proposi- 
tions, in a simple act of reasoning, are only two in 
number ; and it is always required that they be of 
themselves apparent to the understanding, insomuch 
that we assent to and perceive the truth of them as 
soon as proposed. In the syllogism given above, the 
premises are supposed to be self-evident truths, other- 
wise the conclusion could not be inferrsd by a single 
act of reasoning. If, for instance, in ths major, every 
creature possessed of reason and liberty ij accountable 

for Ms actions, the connexion between the subject and 
predicate could not be perceived by a bare attention 
to the ideas themselves ; it is evident, that this propo- 

.sition would no less require a proof, than the conclu- 
sion deduced from it. In this case, a new middle ternt 
must be sought for, to trace the connexion here sup> 
posed; and thi§>>f course furnishes another syllogism, 
by which, having established the proposition in ques^ 
tion, we are thea, and not before, at liberty to use it 
in any succeeding train of reasoning. And should it 
so happen, that m this second essay, there was still 



ELEMENTS OF LOGIC. 136 

same previous proposition whose truth did not appear 
at first sight ; we must then have recourse to a third 
syllogism, in order to lay open that truth to the mind f 
because so long as the premises remain uncertain, the 
conclusion built upon them must be so too. When by 
conducting our thoughts in this manner, w« at last 
arrive at some syllogism, where the previous proposi- 
tions are intuitive truths ; the mind then rests in full se- 
curity, as perceiving that the several conclusions it has 
passed through, stand upon the immovable foundation 
o( self-evidence, and, when traced to their source, ter- 
minate in it. 

Sec. IX... .Reasoning, in the highest exercise of it^ only 
a Concatenation of Syllogisms. 

We see, therefore, that in order to infer a conclu- 
sion by a single act of reasoning, the premises must 
be intuitive propositions. Where they are not, pre- 
vious syllogisms are required, in which case reasoning- 
becomes a complicated act, taking in a variety of suc- 
cessive steps. This frequently happens in tracing the 
more remote relations of our ideas, where many mid- 
dle terms being called in, the conclusion cannot be 
made out, but in consequence of a series of syllogisms 
following one another in train. But aUhough in this 
coiicatenation of propositions, those that form the pre- 
mises of the last syllogism, are often considerably re- 
moved from self-evidence ; yet if we trace the reason- 
ing backwards, we shall find them the conclusions of 
previous syllogisms, whose premises approach nearer 
and nearer to intuition, in proportion as we advance, 
and are found at last to terminate in it. And if after 
having d]us unravelled a demonstration, we take it the 
contrary way, and observe how the mind, setting out 
with intuitive perceptions, couples them together to 
form a conclusion — how, by introducing this conclu- 
sion into another syllogism, it still advances one step 
farther ; and so proceeds making every new discovery- 
subservient to its future progress — we shall then per- 
ceive clearly, that reasoning, in the highest exercise 
of tUat faculty, h no fliore than an orderly combina- 



136 ELEMENTS OF LOGIC. 

tion of thos«^ simple acts, which we have already so 
fully explaihed. The great art lies, in so adjusting 
our syllogisms one to another, that the propositions se- 
verally made use of, as premises, may be manifest con- 
sequences of what goes before. For as by this means, 
every conclusion is deduced from known and establish- 
ed truths, the very last in the series, how far soever we 
carry it, will have no less certainty attending it, than 
Jhe original intuitive perceptions themselves, in which 
the whole chain of syllogisms takes its rise. 

Sec. X Requires intuitive Certainty in every Step of 

the Progression. 

Thus we see, that reasoning beginning with first prin- 
ciples, rises gradually from one judgment to another, 
and connects them in such manner, that every stage 
of the progression brings intuitive certainty along with 
it. And now at length we may clearly understand 
the definition given above, of this distinguishing facul- 
ty of the human mind. Reason, we have said, is the 
ability of deducing unknown truths, from principles 
or propositions that are already known. This evident- 
ly appears, by the foregoing account, where we see, 
that no proposition is admitted into a syllogism, to serve 
as one of the previous judgments on which the conclu- 
sion rests, unless it is itself a known and established 
truth, whose connexion with self-evident principles has 
been already traced. 

Sec. XI,... Self- evident Truths, the ultimate Foundation 
of all Science and Certainty. 

There is yet another observation which naturally of- 
fers itself, in consequence of the above detail ; viz* 
that all the knowledge acquired by reasoning, how far 
soever we carry our discoveries, is still built upon our 
intuitive perceptions. * Towards the end of the last 
part, we divided propositions into self-evident and de- 
monstrable, and represented those of the self-evident 
kind, as the foundation on which the whole super- 
structure of human science rested. This doctrine is 
now abundantly confirmed by what has been delivered 



ELEMENTS OT LOGIC. 137 

ifi the present chapter. We have found, that every 
discovery of human reason, is the consequence of a 
train of syllogisms, which, wiien traced to their source, 
ahvays terminate in self-evident perceptions. When 
the mind arrives at these primitive truths, it pursues 
not its inquiries farther, as well knowing, that no 
evidence can exceed that which flows from an imme- 
diate view of the agreement or disagreement between 
its ideas. And hence it is, that in unravelling any part 
of knowledge, in order to come at the foundation on 
which it stands, intuitive truths are always the last 
resort of the understanding, beyond which it aims not 
to advance, but possesses its notions in perfect security 
as. having now reached the very spring and fountain of 
all science and certainty. 



CHAP. II. 

OF THE SEVERAL KINDS OF REASONING, AND FIRST 
OF THAT BY WHICH WE DETERMINE THE GENERA 
AND SPECIES OF THINGS, 

Sec. 1.... Reasoning Twofold. 

We have endeavoured, in the foregoing chapter, 
to give as distinct a notion as possible, of reason- 
ing, and of the manner in which it is conducted. Let 
us now inquire a little into the discoveries made by 
this faculty, and what those ends are, which we have 
principally in view^ in the exercise of it. All the aims 
of human reason may in the general, be reduced to 
these two : 1. To rank things under those universal 
ideas to which they truly belong ; and 2. To ascribe to 
ihem their several attributes and properties, in conse- 
quence of that distribution. 

Sec. II.,., The fir at kind regards the Genera and Spe- 
cies of things. 

First, then I say, that one great aim of human rea^ 
son is, to determine the genera and species of things. 
We have seen, in the first part of this treatise, how 
the mind proceeds in framing general ideas. We have 
'^Isoseen, in the second part, how, by means of these- 



138 ELEMENTS OF LOGIC- 

general ideas, we come by universal propositions. Now 
as in these universal propositions, we affirm some pro- 
perty of a genus or species, it is plain, that we cannot 
apply this property to particular objects, till we have 
first determined, v/hether they are comprehended un- 
der that general idea, of which the property is affirm- 
ed. Thus there are certain properties belonging to all 
e^yen numbers vvhicli nevertheless cannot be applied to 
anj'' particular number, until we have first discovered 
it to be of the species expressed by that general name. 
Hence reasoning begins with referring things to their, 
several divisions and classes in the scale of our ideas ;, 
and as these divisions are all distinguished by pe- 
culiar names, we hereby learn to apply the terms ex- 
pressing general conceptions, to such particular objects,, 
as come under our immediate observation. 

Sec .iii....T/ie Steps by which we arrive at canclu^ 
sions of' this sort. 

Now in order to arrive at these conclusions, by which 
the several objects of perceptions are brought under 
general names, two things are manifestly necessary. 
First, that we take a viewofthe idea itself denoted by 
that general name, and carefully attend to the distin- 
guishing marks which serve to characterise it. Se- 
condly, that we compare this idea with the object un- 
der consideration, observing diligently wherein they 
ogree or differ. If the idea is found to correspond 
>vi(h the particular object, we then, without hesitationv 
upply the general name ; but if no such correspondence 
intervenes, the conclusion must necessarily take a con- 
trary turno . Let us, for instance, take the number. 
eight, and consider by what steps we are led to pro- 
nounce it an even number. , First then we call to mind 
the idea signified by the expression, an even number ^ 
viz. ih'di it is a number divisible into tza^ a equ,al parts. 
VVe then compare this idea with the number ei^/i^,.am:l. 
tinding them manifestly to agree, see at once the ne- 
cessity of admitting the conchisfon. These several 
judgments tlierefore, transferred into language, and re- 
duced to tiie form of a syDogism, appear thus : 



CLEMENTS or LOGIC. 130 

Every number that may Le divided into two equal pr.rts, is an even 
i);:inber. 
Tiie number eijA/ nmy be clivitled into two equal paits. 
Therel'ore the iiuixiber ci^hl is an tvcn number. 

Sec IV. ...Those steps always follozved,, though in fa- 
miliar cases we do not always attend to them. 

I have made choice of this example, not so much for 
the sake of the conclusion, which is ohvious enoug'a 
and might have been obtained without all that parade 
of words ; but chiefly because it is of easy compre- 
hension, and serves, at the same time distinctly to ex- 
hibit the form of reasoning by which the understand- 
ing; conducts itself in all instances of this kind. And 
here it may be observed, that where the general idea, to 
which particular objects are referred, is very familiar 
to the mind, and frequently in view ; this reference,, 
and the application of the general name, seem to b^ 
made without any apparatus of reasoning. When we. 
^ee a horse in the fields, or a dog in the. street, wsv 
readily apply the name of the species ; habit, and a- 
familiar acquaintance with the general idea, suggest- 
ing it instantaneously to the mind. We are not,, 
however, to imagine on this account, that the nrider- 
standing departs from thci usual rules cf just thinking. 
A frequent repetition of acts begets a habit ; and ha-, 
bits are attciicred with a certain promptness of execution^ 
that prevents our observing the several steps and gra- 
dations, by which any course of action is accomplish- 
ed. . But in other instances, where we judge not bjr 
precontracted habits, as when. the. general idea is very 
complex, or less familiar to. the mind ; we always pro- 
ceed according to the . form of reasoning established 
above. A goldsmith, for instance, who is in doubt as 
to any piece of metal, whether it be of the species^ cal- 
led g-o/(i, first examines its properties, and then com- 
paring them, with the general idea signified by that 
name, if he find a perfect correspondence, no longer 
hesitates under what class of metals to rank it. Now^ 
what js this, but following step by step those rules of 
reasoning, which we have before laid down as the stand- 



140 ELEMENTS OF LOGIC. 

ards, by which to regulate our thoughts in all corcIu- 
sionsof this kind ? 

Sec. V The Great Importance of this Branch of 

Reasoning. 

Nor let be imagined, that our researches here, be- 
cause in appearance bounded to the imposing of gene- 
ral names upon particular objects, are therefore trivi- 
al and of little consequence. Some of the most consi- 
derable debates among mankind, and such too, as 
nearly regard their lives, interest, and happiness, turn 
wholly upon this article. Is it not the chief employ- 
ment of our several courts of judicature, to determine, 
in particular instances, what is law, justice, and equi- 
ty ? Of what importance is it, in many cases, to decide 
aright, whether an action shall be termed murder or 
manslaughter ? We see, that no less than the lives and 
fortunes of men depend often upon thtse decisions. 
The reason is plain. Actions, when once referred to k 
general idea, draw after them all that may be affirmed 
of that idea ; insomuch that the determining the species 
of actions, is all one with determining what proportion 
of praise or dispraise, commendation or blame, &c. 
aught to follow them. For as it is allowed that murder 
deserves death, by bringing any particular action under 
the head of murder, we of course decide the punishment 
due to it. 

Sec. VI, ...And the exact observance of it practised by 
•^ Mathematicians. 

But the great importance of this branch of reason- 
ing, and the necessity of care and circumspection, in 
referring particular objects to general ideas, is Still far- 
ther evident from the practice of the mathematicians. 
Every one who has read Euclid, knows, that he fre- 
quently requires us to draw lines through certain points, 
and according to such and such directions. The fi- 
gures thence resulting are often squares, parallelo- 
grams, or rectangles. Yet Euclid never supposes this 
from their bare appearance, but always demonstrates it 
vpon the strictest principles of geometry. Nor is the 
method he takes, m any thing diiFerent from that des= 



ELEMENTS OF LOGIC. 141 

cribed above. Thus, for instance, having defined a 
square to be a figure bounded by four equal sides, join- 
ed together at right angles : when such a figure arises 
in any construction previous to the demonstration of a 
proposition, he yet never calls it by that name, until he 
has shown that the sides are equal, and all its angles 
right ones. Now this is apparently the same form of 
reasoning we have before exhibited, in proving eight to 
be an even number ; as will be evident to any one who 
reduces it into a regular syllogism. I shall only add, 
that when Euclid has thus determined the species of 
any figure, he is then, and not before, at liberty to as- 
cribe (o it all the properties already demonstrated of 
that figure, and thereby render it subservient to the fu- 
ture course of bis reasoning. 

Sec. VII Fixed and invariable Ideas, with a steady 

application of Names, renders this part of Knowledge 
both easy and certain. 

Having thus sufficiently explained the rules by which 
we are to conduct ourselves, in ranking particular ob- 
jects under general ideas, and show their- conformity to 
the practice and manner of the mathematicians ; it re- 
mains only to observe, that the true way of rendering 
this part of knowledge both easy and certain, is, by 
habituating ourselves to clear and determinate ideas, 
and keeping them steadily annexed to their respective 
names. For as all our aim is, to apply general word^- 
aright, if these words stand for invariable ideas, that 
are perfectly known to the mind, and can be readily 
distinguished upon occasion, there will be little danger 
of mistake or error in our reasonings. Let us suppose, 
that by examining any object, and carrying our atten- 
tion successively from one part to another, we have ac- 
quainted ourselves with the several particulars observa- 
ble in it. If among these we find such as constitute 
some general idea, framed and settled beforehand by 
the understanding and distinguished by a particular 
name ; the resemblance, thus known and perceived, 
necessarily determines the species of the object, and 
thereby gives it a right to the name by which that spe- 



142 ELEMENTS OF LOGIC. 

•cies is called. Thus, four equal sides, joined together 
at right angles, make up the notion of a square. As 
this is a fixed and invariable idea, without wh?cb the 
general name cannot be applied, we never call any par- 
ticular figure a squarely until it appears to have these 
several conditions ; and contrariiy, wherever a figure 
is found with these conditions, it necessarily takes the 
name of a square. The same will be found to hold in 
all our other reasonings of this kind ; where nothing 
can create v^iiy difficulty but the want of settled ideas. 
If, for instance, we have not determined within our- 
selves, the precise notion denoted by the word mati' 
slaughter^ it will be impossible for us to decide, whe- 
ther any particular action ought to bear that name : be- 
cause, however nicely we examine the action itself, yet 
being strangers to the general idea with which it is to 
be compared, we are utterly unable to judge of their 
agreement or disagreement. But if we take care to re- 
move this obstacle, and distinctly trace the two ideas 
under consideration, all difficulties vanish, and the re- 
solution becomes both easy and certain. 

Sec. viu..>,iBy such a Conduct, Certainty and Demon' 
stration might be introduced into other Parts of Know- 
ledge as well as Maihematics. 

Thus we see of what importance it is, towards the 
improvement and certainty of human knowledge, that 
we accustom ourselves to clear and determinate ideas, 
and a steady application of words- Nor is this so easy 
a task as some may, perhaps, be apt to imagine ; it re- 
quiring both a comprehensive understanding, and great 
command of attention, to settle the precise bounds of 
our ideas, when they grow to be very complex, and 
include a multitude of particulars. Nay, and after 
these limits are duly fixed, there is a certain quickness 
of thought and extent of mind required, towards keep- 
ing the several parts in view, that in comparing our 
ideas one with another, none of them may be over- 
k)oked. Yet ought not these difficulties to discourage 
us ; though great, they are not unsurmountable, and 
the advantages arising from success will amply recom^ 



ELEMENTS QV LOGIC. H3 

pense our toil. The certainty and easy application of 
mathematical knowledge is wholly owing lo ihe exact 
observance of this rule. And I am apt lo imagine, 
that if we were to employ the same care about ail our 
other ideas, as mathematicians have done about those 
of number and magnitude, by forming them into exact 
combinations, and distinguishing these combin:^tio'!S by 
particular names, in order to keep them steady and in- 
variable ; we would soon have it in our power to intro- 
duce certainty *aid demonstration into other parts of hu- 
man knowledge. 



«o:: 



CHAP. III. 

OF REASONING AS IT REGARDS THE POWERS AND PRO- 
PERTIES OF THINGS, AND THE RELATIONS OF OUR 

GENERAL IDEAS. 

Sec. I The Distinction of reasoning «.<? it regards ihe 

Sciences and a$ it concerns common Life. 
We com^; now to the second great end wiiich men 
have in view in their reasonings, namely, the discover- 
ing and ascribing to things their several attributes and 
propenies. And here it w-'l be necessary to distin- 
guish betw^een re3soning, as it regards the sciences, and 
as it c ncerns common life. In the sciences our reason 
is employed chieiiy ab mi- univeisa) truths, it being by 
tiiem alone that the bounds of human knowledge are 
eniarffed. Hence the division of things into various 
classes, called otherwise genera and species. For these 
universal ideas, beitig set up as the representatives of 
man}' particular thi.igs, whatever is affirmed of them, 
may also be ^.ffir iied of all the individuals to which they 
belong. yi'itrrJer, for instance, is a general idea, ve^- 
resenting a certain species of hum.ai actions. Rc3asoii 
telis uSj fliat the punishment due to it is deith. H^ nee 
every particular action coming under the notion of ? mr- 
der, has the punishment of death al lolled to it. Here 
then we apply the general truth to some obvious in- 
stance, and tliis is what properiy constituies the rer.son- 
iag of common life. For men in their ordmary trans- 



H4 ELEMENTS OF LOGIC. 

actions and intercourse one with another, have, for Uie 
most part to do only with particular objects. Our 
friends and relations, their characters and behaviours, 
the constitution of the several bodies that surround us, 
and the uses to which they may be applied, are what 
chiefly engage our attention. In all these we reason 
about particular things ; and the whole result of our rea- 
soning is, the applying the general truths of the scien- 
ces to the ordinary transactions of human life. When 
we see a viper, we avoid it. Wherever *,Ye have occa- 
sion for the forcible action of water, to move a body 
that makes considerable resistance, we take care to 
convey it in such a manner, that it shall fall upon the 
object with impetuosity. Now all this happens, in con- 
sequence of our familiar and ready application of these 
two general truths : the bite of a viper is mortal : water 
Jailing on a body with impetuosity, acts very forcibly to- 
wards setting it in motion. In like manner, if we set 
ourselves to consider any particular character, in order 
to determine the share of praise or dispraise that be- 
longs to it, our great concern is, to ascertain exactly the 
proportion of virtue and vice. The reason is obvious. 
A just determination, in all cases of this kind, depends 
entirely upon an application of these maxims of morali- 
ty : virtuous actions deserve praise : vicious actions de- 
serve blame. 

Sec II The steps by which we proceed in the Reason- 
ing of common Life. 

Hence it appears that reasoning, as it regards com- 
mon life, is no more than the ascribing the general pro- 
perties of things to those several objects with which 
we are immediately concerned, according as they are 
found to be of that particular division or class to 
which the properties belong. The steps, then, by which 
we proceed, are manifestly these. First, we i-efer the 
object under consideration to some general idea or 
class of things. We then recollect the several attri- 
butes of that general idea ; and, lastly, ascribe all 
those attributes to the present object. Thus in consi- 
dering the character of Sempronius, if we find it to be 



ELEMENTS OF LOGIC, 145 

of the kind called virtuous; when we at the same time 
reflect, that a virtuous character is deserving of esteem, 
it naturally and obviously follows, that Sempronius is 
so too. These thoughts put into a Syllogism, in or- 
der to exhibit the form of reasoning here required run 
thus : 

Every viriuous rmn is worthy of esteem, 

!:cmpro7iiuit is a virtuous man : 

Therefore Scr7.pTonius is worll'j' of es^teem. 

Sec. Jn....l7ie (^onrLCxion and Dependence of ike two 
grand Branches of Reasoning one upon another, 
l^j ih\s syllogism it appears, that before we affirm 
any thing of a particular object, that object must be 
referred to some general idea, Sempronius is pronounced 
worthy of esteem, only in consequence of his being a 
virtuous man, or coming under that general notion. 
Hence we see the necessary connexion of the various 
parts of reasoning, and the dependence they have one 
upon another. The determining the genera and spe- 
cies of things is, as we have said, one exercise of hu- 
raan reason ; and here we find that this exercise is the 
first in order, and previous to the other, vv'hich con- 
sists in ascribing to them their powers, properties, and 
relations. But when we have taken this previous step, 
and brought particular objects under general names ; 
as the properties we ascribe to them are no other than 
thoscof the general idea, it is plain, that in order to a 
successful progress in this part of knowledge, we must 
thoroughly acquaint ourselves with the several rela- 
tions and attributes of these our general ideas. When 
this is done, the other part will be easy, and require 
scarce any lobour of thought, as being no more than 
an application of the general form of reast.-.ing repre- 
sented in the foregoing syllogism. Now, as we have 
already sufficiently shown, how we are to proceed in 
determining the genera and species of things, which 
as we have said, is the previous step to this second 
branch of human knowledge ; all that is farther want- 
ing to a due explanation of it is, to offer some consi- 
derations, as to the nunner of investigating the ge- 
neral relations of our ideas. This 13 the highest exer- 
N 



J 46 ELEMENTS OF LOGIC. 

ciseofthe powers of the understanding, and that by 
means wnereof, we arrive at the discovery of univer- 
sal truths ; insomuch that our deductions in this wajj 
constitute that particular species of reasoning, which, 
we have before said, regards principally the sciences 

Sec. IV.... Two things required to make a good Rea- 
soner 
But that we may conduct our thoughts with some 
order and method, we shall begin with observing, that 
the relations of our general ideas are of two kinds. 
Either such as immediately discover themselves, upon 
comparing the ideas one with another ; or such, as be- 
ing more remote and distant, requires art and contriv- 
ance to bring them into view. The relations of the 
first kind, furnish us with intuitive and self-evident 
truths : those of the second are traced by reasoning, 
and a due application of intermediate ideas. It is of 
this last kind that we are to speak here, having dis- 
patched what was necessary with regard to the other 
in the second part. As therefore in tracing the more 
distant relations of things, we must always have re- 
course to intervening ideas, and are more or less suc- 
cessful in our researches, according to our acquaintance 
with these ideas, and ability of applying them ; it is 
evident, that to make a good reasoner two things are 
principally required. First, an extensive knowledge 
of those intermediate ideas by means of which things 
may be compared one with another. Secondly y the ski!! 
and talent of applying them happily, in all particular 
instances that come under consideration. 
Sec. v....Fi7^st, an extensive Knowledge of intermedi- 
ate Ideas. 
First, I say that in order to our successful progress 
in reasoning, we must have an extensive knowledge of 
those intermediate ideas by means of which things may 
be compared one with another. For as it is not every 
idea that will answer the purpose of our inquiries, but 
such only as are peculiarly related to the objects about 
which we reason, so as by a comparison with them, to 
furnish evident and known truths ; nothing is mom 



ELEMENTS Or LOGIC. 147 

apparent, than that the greater variety of conceptions 
we can call into view, the more likely we are to find 
some among them that will help us to the truths here 
required. And indeed it is found to hold in experience, 
that in proportion as we enlarge our view of things, and 
grow acquainted with a multitude of different objects, 
the reasoning quality gathers strength. For by extend- 
ing our sphere of knowledge, the mind acquires a cer- 
tain force and penetration, as being accustomed to ex- 
amine the several appearances of its ideas, and observe 
what light they cast one upon another. 

Sec. VI To excel inany one Branch of Learnings we 

must in general he acquainted with the whole circle of 
Arts and Sciences. 

And this I take to be the reason, that in order to 
excel remarkably in any one branch of learning, it is 
necessary to have at least a general acquaintance with 
the Vvhoie circle of arts and sciences. The trutli 
of it is, all the various divisions of human knowledge 
are very nearly related among themselves, and, innu- 
merable instances" serve to illustrate and set off each 
<:)ther. And although it is not to be denied, that by 
an obstinate application to one branch of study, a mau 
may make considerable progress, and acquire some de- 
gree of eminence in it ; yet his views will be always 
narrow and contracted, and he will want that master- 
ly discernment v»'hich not only enables us to pursue 
our discoveries with ease, but also in laying them open 
to others, to spread a certain brightness around them. 
! would not, however, here be understood to mean, 
that a general knowledge alone is sufficient for ail the 
purposes of reasoning. I only recommend it as pro- 
per to give the mind a certain sagacity and quickness, 
and qualify it for judging aright in the ordinary oc- 
currences of life. But when our reasoning regards a 
particular science, it is farther necessary, that we more 
nearly acquaint ourselves with whatever relates to that 
science. A general knowledge is a good preparation, 
and enables us to proceed with ease and expedition in 
whatever branch of learning we apply to. But then . 



148 ELEMENTS OF LOGIC 

in the minute and intricate questions ef any science^, 
we are by no means qualified to reason with advantage, 
until we have perfectly mastered the science to which 
they belong ; it being hence chiefly that we are furnish- 
ed with those intermediate ideas, which lead to a jusi 
and successful solution. 

^Kc. VII Why Mathematicians sometimes ansi^er not 

the expectation their great learning raises. 

And here as it comes so naturally in my way, I can- 
not avoid taking notice of an obsei-vation that is fre- 
quently to be met with, and seems to carry in it at 
first sight something very strange and unaccountable. 
It is, in short, this, that mathematicians, even such a^ 
are allowed to excel in their own profession, and to 
have discovered themselves perfect masters in the art 
'if reasoning, have not yet been always happy in treat- 
ing upon other subjects ; but rather fallen short, not 
only what might naturally have been expected from 
them, but of many writers much less exercised in the 
rules of the argumentation. This will not appear s© 
very extraordinary, if we reflect on what has been 
hinted above. Mathematics is an engaging study : and 
men who apply themselves that way, so wholly plunge 
into it, that they are for the most part but little ac- 
quainted with other branches of knowledge. When, 
therefore, they quit their favorite subject, and enter 
upon others, that are in a manner new and strange to 
them, no wonder if they find their invention at a 
stand. Because, however perfect they may be in the 
art of reasoning, yet wanting here those intermediate 
ideas which are necessary to furnish out a due train of 
propositions, all their skill and ability fails them. For 
a bare knowledge of the rules is not sufficient. We 
must farther have materials whereunto to apply them. 
And when these are once obtained, then it is that an able 
reasoner discovers his superiority, by the just choice he 
makes, and a certain masterly disposition, that in eve- 
ry step of the procedure carries evidence and convic- 
tion along with it. And hence it is, that such mathe- 
maticians as have of late years applied themselves to 



1 



ELEMENTS OF LOGIC, 149 

Other sciences, and not contented with a superficial 
knou'ledge, endeavoured to reach their inmost recess- 
es ; such mathematicians, I say, have by mere strength 
of mind, and a happy application of geometrical rea- 
soning, carried their discoveries far beyond what was 
heretofore judged the utmost limits of human know- 
ledge. This is a truth abundantly known to all who are 
acquainted with the late wonderful improvements in 
natural philosophy. 

Sec. V III..,.. Secondly^ the Skill of applying Intermedi- 
ate Ideas happily iri particular instances. 

I come now to the second thing required, in order 
to a successful progress in reasoning, namely, the skill 
and talent of applying intermediate ideas happily in 
all particular instances that come under consideration. 
And here I shall not take up much time in laying down 
rules and precepts, because I am apt to think they 
would do but little service. Use and exercise are the 
best instructors in the present case : and whatever lo- 
gicians may boast, of being able to form perfect rea- 
soners by book and rule, yet we find by experience, 
that the study of their precepts does not always add 
any great degree of strength to the understanding. In 
short, tis the habit alone of reasoning ihat makes a 
reasoner. And therefore the true yvay to acquire this 
talent, is, by being much conversant in those sciences 
where the art of reasoning is allowed to reign in the 
greatest perfection. Hence it was, that the ancients, 
who so well understood the manner of forming the 
mind, always began with mathematics as the founda- 
tion of their philosophical studies. Here the under- 
standing is by degrees habituated to truth, contracts 
insensibly a certain fondness for it, and learns never 
to yield its assent, to any proposition, but where the 
evidence is sufficients to produce full conviction. For 
this reason Plato has called mathematical demonstra- 
tions the cathartics or p-tirgatives of the soul, as be- 
ing the proper means to cleanse it from error, aqd re- 
store that natural exercise of its faculties in whiclj, 
iust thinking consists. And indeed I believe. it will 
N 2 . 



150 ELEMENTS OF LOGIC, 

be readily allowed, that no science furnishes so many 
instances of a happy choice of intermediate ideas, and 
a dexterous application of them, for the discovery of 
tralth and enlargement of knowledge. 

Sec. IX The Study of Mathematical Demonstrations- 

of great avail in this respect. 

If, therefore, we would form our minds to a habit of 
reasoning closely and in train, we cannot take auj 
more certain method, than the exercising ourselves in 
mathematical demonitrations, so as to contract a kind 
of familiarity with them, " not that we look upon it 
a's necessary, {To use the words of the great Mr, 
Locke) that all men should be deep mathematicians^ 
but that, having got the way of reasoning which that 
study necessarily brings the mind to, they may be 
able to transfer it to other parts of knov/ledge, as they 
shall have occasion.. For in all sorts of reasoning every 
single argument should be managed as a mathematical 
demonstration, the connexion and dependence of ideas 
should be followed, till the mind is brought to the 
source on which it bottoms, and can trace the cohe- 
rence through the whole train of proofs. It is in the 
general observable, that the faculties of our souls are 
improved and made useful to us just after the same 
manner as our bodfes are»- Would you have a ma» 
write or paint, dance or fence well, or perform any 
other manual operation, dexterously and with ease ? 
Let him have ever so much vigour and activity, sup- 
pleness, and address naturally, yet nobody expects- 
Ihis from him, unless he has been used to it, and has 
employed time and pains in fashioning and forming 
bis hand, or outward parts to these motions. Just so 
it is in the mind J would you have a man reason well, 
you must use him to it betimes, exercise his mind ii* 
observing the connexion, of ideas, and following them 
in train., Nothing does this better than mathematics ; 
iTrhich, tlierefcre, I think should be taught all those 
who have the time and opportunity, not so much to 
make them mathematicians, as to make them reasona^ 

•jIs^ creatures ; for though we all call ourselves so. ban 



ELEMENTS OF LOGIG. 151 

cause we are born to it, if we please ; yet we maj 
truly say, nature gives us but the seeds of it. We are 
born to be, if we please, rational creatures ; but 'tis 
use ani exercise only that makes us so, and we are in- 
deed so, no farther than industry'- and application has 
carried us." Conduct of the Understanding. 

Sec. X As also of such Authors on other Subjects^ as 

are distinguished for Strength and Justness of Rea- 
soning. 

But although the study of mathematics be, of all 
others, the most useful to form the mind and give ii 
an early relish of truth, yet ought not other parts of 
philosophy to be neglected. For there also we meet 
with many opportunities of exercising the powers of 
the understanding ; and the variety of subjects natu- 
rally lead us to observe all those different turns of 
thinking that are peculiarly adapted to the several 
ideas we examine, and the truths we search after» 
A mind thus trained, acquires a certain mastery over 
its own thoughts, insomuch that it can range and mo- 
del them at pleasure, and call such into view as best 
suit its present designs. Now in this the whole art of 
reasoning consists, from among a great variety of dif- 
ferent ideas, to single out those that are most proper 
for the business in hand, and to lay them together in 
such order, that from plain and easy beginnings, by 
gentle degrees, and a continual train of evident truths, 
we may be insensibly led on to such discoveries, as at 
our first setting out, appeared beyond the reach of the 
human understanding. For this purpose, besides the 
study of mathematics before recommended, we ought 
«o apply ourselves dilig^ently to the reading of such 
authors as have distinguished themselves for strength 
»f reasoning, and a just and accurate manner of think- 
ing. For it is observable, that a mind exercised and 
seasoned to truth seldom rests satisfied in a bare con- 
templation o'f the arguments offered by others, but 
will be frequently essaying its own strength, and pur- 
suing its discoveries upon the plan it is most accustom- 
ed Vo. Thus we insensibly contract a haUit of traciBg 



152 ELEMENTS OF LOGIC. 

truth from one stage to another, and of investigating' 
those general relations and properties which we after- 
wards ascrihe to pnrticular things, according as we 
find them comprehended under the abstract ideas to 
which the properties belong. And t'^us having parti- 
cularly shown how we are to distribute the several ob- 
jects of nature under general ideas, what properties 
we are to ascribe to them in consequence of that distri- 
Lution, and how to trace and investigate the properties 
themselves ; I think I have sufficiently explained all 
that is necessary towards a due conception of reason-- 
ing, and shall therefore here conclude this chapter. 



CHAP. IV. 

OF THE FORMS OF SYLLOGISMS. 

Sec. I,.., The Figures of Syllogisms. 

Hitherto we have contented ourselves with a 
general notion of syllogisms, and of the parts of 
which they consist. It is now time to enter a little 
more particularly into the subject, to examine their 
various forms, and to lay open the rules of argumen- 
tation proper to each. In the syllogisms mentioned in 
the foregoing chapters, we may observe, that the mid- 
dle term is the subject of the major proposition, and the 
predicate of the mmor. This disposition, though the 
most natural and obvious, is not however, necessary ; 
it frequently happening, that the middle term is the 
subject in both the premises, or the predicate in both ; 
and sometimes, directlv contrary to its disposition in 
the foregoing chapters, the predicate in the major ^ and . 
the subject in the minor. Hence the distinction of syl- 
logisms into various kinds, QdMedTJigures by logicians. 
Toy figure, according to their use of the word, is no- 
thing else bnt the order and disposition of the middle 
term in any syllogism. A.nd as this disposition is, we 
see, four-fold; so the figures of syllogisms thence aris-. 



ELEMENTS OF LOGIC. 1^.3 

'ing are four in number. When the middle term is the 
subject of the major proposition, and the predicate oi' 
the minor, we have what is called the^r^i figure. If 
o\\ the other hand, it is the predicate of both the pre- 
mises, the syllogism is said to be in the second figure. 
A<^ain, in the ihirdfigure^ the middle term is the sub- 
ject of the two premises. And lastly, by making it the 
predicate of the ?najor, and subject of the minor, we 
obtain syllogisms in the fourthj^^wrc. 

Sec. u....The AIo a ds of Syllogisms. 

But besides this fourfold distinction of syllogisms, 
ihere is also a farther subdivision of them in every fi- 
.cure, arising from the quantity and quality^ as they are 
«;alled, of the propositons. By quantity we mean the 
consideration of propositions as universal or particular ; 
by quality as affirmative or negative. Now as in all the 
several dispositions of the middle term, the propositions, 
©f which a syllogism consists, may be either universal 
or particular, affirmative or negative ; the due determi- 
nation of these, and so putting them together as the 
laws of argumentation require, 'constitute what logi- 
cians call the moods of syllogisms. Of these moods there 
are a determinate number to every figure, including 
all the possible ways in which propositions differing in 
quantity or quality can be combined, according to any 
disposition of the 7n.itZc//e ^er7n, in order to arrive at a 
just conclusion. The shortness of the present work 
will not allow of entering into a more particular des- 
cription of these several distinctions and divisions. I 
shall therefore content myself with referring the rea- 
der to the Port Royal art ofi thinking, where he will 
find the moods and figures of syllogisms distinctly ex- 
plained, and the rules proper to each very neatly de- 
monstrated. 

Sec. in.... Foundation of the other Divisions of Syl- 
logisms. 

The division of syllogisms according to mood and 
figure, respects those especially, which are known by 
the name of plain simple syllogisms ; that is, which ar« 
bounded to three propositions, all simple, and where 



154 ELEMENTS OF LOGIC. 

the extremes and middle term are connected, accord- 
ing to the rules laid down above. But as the mind is 
not tied down to any one precise form of reasoning, 
but sometimes makes use of more, sometimes of few- 
er premises, and oilen takes iii compound and condi- 
tional propositions, it may not be amiss to take notice 
of the different forms derived from this source, and ex- 
plain the rules by which the mind conducts itself in 
the use of them. 

Sec. iv....Con(Ution2il Syllogisms. 
When in any syllogism, the major is a conditional 
proposition, the sjilogism itself is termed conditional. 
Thus : 

If there is a God, he ou^ht to be woi-shipped. 

But there is a God : 

Therefore he ought to he worshipped. 

In this example, the major or first proposition, is we 
see, conditional, and therefore the syllogism itself is 
also of the kind called by that name. And here we 
are to observe, that all conditional propositions are 
made up of two distinct parts ; one expressing the 
condition upon which the predicate agrees or disagrees 
with the subject, as in this now before us, if there is a 
God ; the other joining or disjoining the said predi- 
cate Tind subject, as here, he ought to be worshipped. The 
first of these p^s, or that which implies the condi- 
tion, is called the antecedent: the second, where we 
join or disjoin the predicate and subject, has the namfe 
of the consequent. 
Sec. w....Ground of Illation in conditional Syllogisms. 

These things explained, we are farther to observe, 
that in all propositions of this kind, supposing them 
to be exact in point of form, the relation between the 
antecedent and consequent, must ever be true and 
real ; that is, the antecedent must always contain 
some certain and genuine condition which necessa- 
rily implies the consequent ; for otherwise, the pro- 
position itself will be false, and therefore ought not 
to be admitted into OUT reasonings. Hence it follows, 
that when any conditional proposition is assumed, if 
we admit the antecedent of that proposition, we must, 



ELEMENTS OF LOGIC. 1 55 

at the same time, necessarily admit the consequent : 
bill if we reject the consequent, we are, in like man- 
ner, bound to reject also the antecedent. For as the 
Antecedent always expresses some condition which ne- 
cessarily implies the truth of the consequent ; by ad- 
mitting the antecedent, we allow of that condition, and 
therefore ought also to admit the consequent. In like 
manner, if it appears that the consequent ought to be 
rejected, the antecedent evidently must be so toe ; be- 
cause, as we just now demonstrated, the admitting of 
the antecedent would necessarily imply the admission 
also of the consequent. 

Sec. VI. ...The two Moods of Conditional Syllogism. 

From what has been said, it appears, that there are 
two ways of arguing in hi/pothetical syllogism, which 
lead to a certain and unavoidable conclusion. For as the 
major is always a conditional proposition, consisting of 
an antecedent and a consequent ; if the minor admits 
the antecedent, it is plain, that the conclusion must ad- 
mit the conseqjent. This is called arguing from the 
admission of the antecedent to the admission of the con- 
sequent, and constitute that mood or species oUiypo- 
thetical syllogisms, which is distinguished in the schools 
by the name of the modus ponens, inasmuch as by it the 
whole conditional proposition, both antecedent and con- 
sequent, is established. Thus, 

If God is infinitely wise, and acts with perfect freedom, he doesnotbing 
but what is best. 

But God is infinitely wise, and acts with perfect freedom, 
Tlierefore he does nothing but what is best. 

Here we see the antecedent or first part of the condi- 
tional proposition is established in the minor, and the 
consequent or second part in the conclusion ; whence 
the syllogism itself is an example of the modus ponens. 
But if now we on the contrary suppose, that the minor 
rejects the consequent, then it is apparent, that the 
conclusion must also reject the antecedent. In this case 
we are said to argue from the removal of the consequent, 
to the removal of the antecedent ; and the particular 
mood, or species of syllogism thence arising is called by 



15G ELEMENTS OF LOGIC. 

logicians the modus tollens ; because in it, both antece- 
dent and consequent are rejected or taken away, as ap- 
pears by the fohowing example : 

If God were not a lieing of infinite goodneas, neither would be consult tbe 
bap|':ne?s of his creatures. 
Biit God does consult the happiness of his creatures : 
Therefore He is a Being of Infinite Goodness. 



.They include all the Legitimate Ways of ' 



Argu 



in, 



Tiiese two species take in the whole class of co7idi- 
tional syllogisms, and include all the possible ways of 
arguing that lead to a legitimate conclusion ; because 
we cannot here proceed by a contrary process of rea- 
soning, that is, from the removal of the antecedent to 
the removal of the consequent, or from the establish- 
ing of the consequent to the establishing of the ante- 
cedent. For although the antecedent always expresses 
some real condition, which, once admitted, necessarily 
implies the consequent, yet it does not follow, that 
there is therefore no other condition ; and if so, then, 
after removing the antecedent, the consequent may 
still hold, because of some other determination that in- 
fers it. When we say : If a stone is exposed some time 
to ike rays of the sun, it xmll contract a certain degree of 
heat; the pi-oposition is certainly true, and, admitting 
^he antecedent, we must also admit the consequent. 
But as there are other ways by which a stone may gath- 
er heat, it will not follow from the ceasing of the before- 
me Uioned condition, that therefore the consequent can- 
not tatce place. In other words, we cannot argue, but 
the stone has not been exposed to the rays of the sun ; 
therefore neither has it any degree of heat ; inasmuch as 
there Eire a great many other ways by which heat might 
have been communicated to it. And if we cannot ar- 
gue from the removal of the antecedent to the removal 
of the consequent, no more can we from the admission 
of the consequent to the admission of the antecedent. 
Bee r jy fr the consequent may flow from a great varie- 
ty of oiiTi-L]- suppositions, the allowing of it does not 
delermirr hi precise supposition, but only that some 
Qf them musi; take place. Thus in the foregoing propo- 



ELEMENTS OF LOGIC. 157 

sitiou, if a stone is exposed some time to the rays of the 
swi, it will contract a certain degree of heat ; admitting 
the consequent, viz. that it has contracted a certain de- 
gree of heat, we are not therefore bound to admit the 
antecedent, that it has been some time exposed to the rays 
of the sun ; because there are many other causes whence 
that heat may have proceeded. These two ways of 
arguing", therefore, hold not in conditional syllogisms. 
Indeed where the antecedent expresses the only condi- 
tion on which the consequent takes place, there they 
may be applied with safety ; because, wherever that 
condition is not, we are sure that neither can the conse- 
quent be, and so may argue from the rem.oval of the one 
to the removal of the other ; as, on the contrary, wher- 
ever the consequent holds, it is certain that the condi- 
tion must also take place ; which shows, that by esta- 
blishing the consequent, we at the same time establish 
Ihe antecedent. But as it is a very particular case, and 
that happens but seldom, it cannot be extended into a 
general rule, and therefore affords not any steady and 
universal ground of reasoning upon the two foregoing 
suppositions. 

Sec. VIII The mGLnner of Arguing in Disjunctive Syl- 
logisms. 

As from the major'^s being a conditional proposition, 
we obtain the species of conditional syllogisms ; so 
where it is a disjunctive proposition, the syllogism, to 
which it belongs, is called disjunctive^ as in the follow- 
ing example : 

The world is either self- existent, or the work of some finite or of some 
infinite being. 
But it is not self-existent, nor the work of a finite being: 
Therefore it is the work of an infinite being. 

Now a disjunctive proposition is that where of seve- 
ral predicates we affirm one necessarily to belong to 
the subject, to the exclusion of all the rest, but leave 
that particular one undetermined. Hence it follows, 
that as soon as we determine the particular predicate, 
all the rest are of course to be rejected ; or if we re- 
ject all the predicates but one, that cne necessarily 
O 



158 ELEMENTS OF LOGIC. 

takes place. When, therefore, in a disjunctive syllo- 
gism, the several predicates are enumerated in the ma- 
jor. ...if the minor eStabHshes anyone of these predi- 
cates, the conclusion ought to remove all the rest ; or 
if, in the minor^ all the predicates but ^one are remov- 
ed, the conclusion must necessarily establish that one* 
Thus in the disjunctive syWoghm given above, the ma- 
jor affirms one of three predicates to belong to the 
earth, viz. self-existence, or that it is the work ofajinite^ 
or that it is the work of an infinite being. Two of these 
predicates are removed in the minor, viz. self-existence , 
and the work of a finite being. Hence the conclusion 
necessarily ascribes to it the third predicate, and af- 
firms, that iK'is the work of an infinite being. If now 
we give the syllogism another turn, insomuch that the 
minor may establish one of the predicates, by affirming 
the earth to be the prodiiciioii of an irifnite being.... 
then the conclusion must remove the other two, assert- 
ing it to be neither self-existent, nor the work of a finite 
being. These are the forms of reasoning in this species 
of syllogisms, the justness of which appea];s at first 
sight ; and that there can be no other, is evident from 
the very nature of a disjunctive proposition. 

Sec . IX. , . ..Imperfect or mutilated Syllogisms . 
In the several kinds of syllogisms hitherto mention- 
ed, we may observe, that the parts are complete ; that 
is, the three propositions of which they consist are re- 
presented, in form. But it often happens, that some 
one of the premises is not only an evident truth, but also 
familiar and in the minds of all men ; in which case it 
is usually omitted, whereby we have an imperfect syl- 
logism, that seems to be made up of only two proposi- 
tions. Slibuld we, for instance, argue in this manner : 

Every man is morlal ; 
Therefore every king is mortal •, 

the syllogism appears to be imperfect, as consisting but 
of two propositions. Yet it is really complete, only the 
minor [every king is a man] is omitted, and left to the 
reader to supply, as being a proposition so familiar and 
evident, that it cannot escape him. 



ELEMENTS OF LOGIC, 159 

Sec. •K....Enthymemes. 

These seemingly imperfect syllogisms are called 
Enthymeines, and occur very frequently in reasoning, 
tf^specially where it makes a part of common conversa- 
tion. Nay, there is a particular elegance in them, be- 
cause not displaying the arguments in all its parts, 
they leave somewhat to the exercise and invention of 
the mind. B3" this means we are put upon exerting 
ourselves, and seem to share in the discovery of what 
is proposed to us. Now this is the great secret of fine 
writing, so to frame and put together our thoughts, 
.!i? to give full play to the reader's imagination, and 
draw him insensibly into our very views and course of 
reasoning. This gives a pleasure not unlike to that 
which the author himself feels in composing. It besides 
shortens discourse, and adds a certain force and liveli- 
ness to our arguments, when the words in which they 
are conve3''ed, favour the natural quickness of the mind 
in its operations, and a single expression is left to ex- 
iiibit a whole train of thoughts. 

Sec. lii.... Ground of Reasoning in immediate Conse- 
quences. 

But there is another species of reasoning with two 
propositions, which seems to be complete in itself, and 
where we admit the conclusion, without supposing any 
tacit or suppressed judgment in the mind, from which 
it follows syllogistically. This happens between pro- 
positions where the connexion is such, that the admis- 
sion of the one, necessarilly, and at the first sight, im- 
plies the admission also of the other. For if it so falls 
out, that the proposition, on which the other depends, 
is self-evident, we content ourselves with barel^^ affirm- 
ing it, and infer that other by a direct conclusion. 
. Thus, by admitting an universal proposition, we are 
forced also. to admit of all the particular propositions 
comprehended under it, this being the very condition 
that constitutes a proposition universal. If then that 
universal proposition chances to be self-evident, the 
particular ones follow of course, v/ithout any farther 
train of reasoning. Whoever allows, for instance, 



160 ELEMENTS OF LOGIC. 

thdit things equal to one and the same thing are equal to- 
one another, must at the same time allow, that two tri- 
angles, each equal to a square, whose side is three 
inches, are also equal between themselves. This argu- 
ment therefore, 

Things equal to one and the same thing, are equal to onp another. 
Therefore those two triangles, each equal to the square of a line Of 
three inches, are equal between themselves; 

is complete in its kind, and contains all that is neces- 
sary towards a just and legitimate conclusion. For the 
first or universal proposition is self-evident, and there- 
tore requires no farther proof. And as the truth of the 
particular i5 inseparably connected with that of the 
umversal, it follows from it by an obvious and unavoid- 
able consequence o ^ 

Sec. xu...,AU reducible to Syllogisms of some one 
form or other. 

Now in all cases of this kind where prepositions are 
ffleduced one from another, 0*1 account of a known and 
evident connexion, we are said to reason by immediate 
consequence. Such a coherence of propositions, mani- 
fest at first sight, and forcing itself upon the mind, fre- 
quently occurs in reasoning. Logicians have explain- 
ed at some length, the several suppositions upon which 
-it takes place, and allow of all immediate consequences 
that follow in conformity to them. It is, however, ob- 
servable, that these arguments, though seemingly com- 
plete, because the conclusion follows necessarily from 
the single proposition that goes before, may yet be 
considered as real enthymemes, whose major, which 
is a conditional proposition, is wanting. The syllo- 
gism but just mentioned, when represented according to 
this view will run as follows : 

If things equal to one and the same thinj are equal to one another-. 

these two triangles, each equal to a square whose side is three 

inches, are also equal between themselves. 
Bat things equal to one atid the same thing, are equal to one another; 
Therefore also these triangles, l;i.. are equal between theoiselires 



ELEMENTS or LOGIC. 161 

This observation will be found to hold in all immedi^ 
ate consequences whatsoever, insomuch that they arc 
in fact no more than enthymemes of hypothetical sj'l- 
logisms. But then it is particular to them, that the 
ground, on which the conclusion rests, namely, its co- 
herence with the minor, is of itself apparent, and seen 
immediately to flow from the rules and reasons of logic. 
As it is, therefore, entirely unnecessary to express a 
self-evident connexion, the major, whose office that is, 
is-<:onstantly omitted; nay, and seems so very little 
needful to enforce the conclusion, as to be accounted 
commonly no part of the argument at all. It must 
indeed be owned, that the foregoing- immediate conse- 
quence might have been reduced to a simple, as well 
as an hypothetical syllogism. This will be evident to 
any one who gives himself the trouble to make the ex- 
periment. But it is not my design to enter farther in- 
to these niceties, what has been said sufficing to show, 
that all arguments consisting of but two propositions, 
are real enthymemes, and reducible to complete syllo- 
gisms of some one form or other. As, therefore, the 
ground on which the conclusion rests, must needs be 
always the same with that of the syllogisms to which 
they belong, we have here an universal criterion, 
whereby at all times to ascertain the justness and valid- 
ity of our reasonings in this way. 

Sec. XIII... .^ Sorites of plain'' simple Syllogisms. 

The next species of reasoning we shall take notice 
of here, is what is commonly knov/n by the name of a 
sorites. This i* a way of arguing, in which a great 
num-ber of propositions are so linked together, that the 
prv^dicate of one becomes continually'the subject of the 
n^xt following, until at last a conclusion is formed, by 
bringing together the subject of the first proposition 
and the predicate of the last. Of this kind is the fol- 
lowing argument : 

God is omnipotent: 

An omnipotent being caa do every thing possible, 

He that, can do every thing possible, can do whatever jnvolres not 

a contradictioc. 
T'^f'fefcre Gcd can do ivbatever involves D(y. a coetraiiction, 

O 2 



1Q2 ELEMENTS OF LOGIC* 

This particular combination of propositions may Be 
continued to any length we please, without in the least 
weakening the ground upon which the conclusion rests. 
The reason is, because the sorites itself may be resolv- 
ed into as many simple syllogisms as there are middle 
terms in it ; where this is found universally to hold, 
that when such a resolution is made, and the syllogisms 
are placed in train, the conclusion of the last in the 
series is also the conclusion of the sorites. This kind 
of argument, therefore, as it serves to unite several syl- 
logisms into one, must stand upon the same foundation 
with the syllogisms of which it consists ; and is, in- 
deed, properly speaking, no other than a compendious 
way of reasoning syllogistically. Any one may be sa- 
tisfied of this at pleasure, if he but takes the trouble of 
resolving the foregoing sorites into two distinct syllo- 
gisms. For he will there find, that he arrives at the 
same conclusion, and that, too, by the very same train 
of thinliing but with abundantly more words, and the 
addition of two superfluous propositions. 

Sec. xiv....j3 Sorites of Hypothetical Syllogisms. 

What is here said of plain simple propositions, may 
be well applied to those that are conditional ; that is, 
any number of them may be so joined together in a 
series, that the consequent of cne, shall become contin- 
ually the antecedent jof the next following ; in which 
case, by establishing the antecedent of the first propo- 
sition, we establish the consequent of the last, or by 
removing the last consequent, remove also the first an- 
tecedent. This way of reasoning is exemplified in the 
following argument : 

If we love any person, all emotions of hatred towards him cease. 

If all emotions of hatred towards a perBOn-cease, we cannot rejoice in his 

misfortunes. 
If we rejoice not in hia misfortunes, we certainly wish him no injury. 
Therefore if we love a person, we wish him no injury. 

It is evident that this sorites, as well as the last, may 
be resolved into a series of distinct syllogisms, with 
this only difference, that here the syllogisms, are all con- 



ELEMENTS OF LOGIC. 263 

ditional. But as the conclusion of the last syllogism in 
the series is the same with the conclusion of the sorites, 
it is plain, that this also is a compendious way of rea- 
soning, whose evidence arises from the evidence of the 
several single syllogisms into which it may be resolved. 

Sec. XV The Ground of Reasoning by Induction. 

I come now to that kind of argument, which logicians 
call induction; in order to the right understanding 
of which, it will be necessary to observe, that our ge- 
neral ideas are for the most part capable of various sub- 
divisions. Thus the idea of the lowest species may be 
subdivided into its several individuals ; the idea of anj' 
genus, into the diflferent species it comprehends ; and 
£0 of the rest. If then we suppose this distribution to 
be duly made, and so as to take in the whole extent of 
the idea to which it belongs ; then it is plain, that aJI 
the subdivisions or parts of any idea taken together con- 
stitute that whole idea. Thus the several individuals 
of any species taken together constitute the whole spe- 
cies, and all the various species comprehended under 
any genus, make up the whole genus. This being al- 
lowed, it is apparent that whatsoever may be affirmed 
of all the several subdivisions and classes of any idea, 
•ught to be affirmed of the whole general idea to which 
these subdivisions belong. What may be affirmed of 
all the individuals of any species, may be affirmed of the 
whole species ; and what may be affirmed of all the 
species of any genus, may also be affirmed of the whole 
I genus ; because all the individuals, taken together, are 
the same with the species, and all the species taken to- 
gether, the same with the genus. 

Sec. XVI The Form and Structure oj an argument 

by Induction. 

This way of arguing, where we infer universally 
concerning any idea, what we had before affirmed or 
denied separately, of all its several subdivisions and 
parts, is called reasoning by induction. Thus if we sup- 
pose the whole tribe of animals, subdivided into men, 
beasts, birds, insects, and fi§^©s, aad then reason con- 



164 ELEMENTS OF LOGIC. 

cernmg them after this manner : All menfvaveapower 
of beginning motion; all beasts, birds, and insects^ 
have a power of beginning motion ; all Jishes have a 
power of beginning motion ; therefore all animals have 
a power of beginning motion : The argument is an in- 
duction. When the subdivisions are just, so as to take 
in the whole general idea, and the enumeration is per- 
fect, that is, extends to all and every of the inferior 
classes or parts ; there the induction is complete, and 
the manner of reasoning by induction is apparently con- 
clusive. 

Sec. XYii,.,.The Ground of Argumentation in a Di- 
lemma^ 

The last species of syllogisms I shall take notice of, 
in this chapter, is that commonly distinguished by the 
name of a dilemma. A dilemma is an argument by 
which we endeavour to prov« the absurdity or falsehood 
of some assertion. In order to this we assume a condi- 
tional proposition ; the antecedent of which is the as- 
sertion to be disproved and the consequent a disjunc- 
tive proposition, enumerating all the possible suppo- 
sitions upon which that assertion can take place. If 
then it appears, that all these several suppositions 
ought to be rejected, it is plain that the antecedent, or 
assertion, itself, must be so too. When, therefore, such 
a proposition as that before-mentioned, is made the ma- 
jor of any syllogism — if the minor rejects all the suppo- 
sitions contained in the consequent, it follows necessari- 
ly, that the conclusion ought to reject the antecedent, 
which, as we have said, is the very assertion to be dis- 
proved. This particular way of arguing, is that which 
logicians call a diVemma; and from the account here 
given of it, it appears, that we may in general define 
it {o he 2in hypothetical syllogism, where the consequent 
of the major is a disjunctive proposition, which is wholly 
taken away or removed in the minor. Of this kind is 
the following : 

If God did not create the world perfect in its kind, it must either proceed 
from want of inclination, or from want of power. 

But it could Dot proceed either from want of inclinatiou, or fromwaBtof 
fower. 



ELEMENTS OF LOGIC. ^65 

Therefore he created the world perfect in its kind. Or tvhich is the same 
thing : 'Tis absurd to say that he did not create the world perfect in its kiuc-. 

Sec. XVIII Jin universal description of it. 

The nature then of a dilemma is universally this. 
The major is a conditional proposition, whose conse- 
quent contains all the several suppositions upon which 
the antecedent can takfe place. As, therefore, these 
suppositions are wholly removed in the minor, it is 
evident, that the antecedent must be so too ; insomuch 
that we here always argue from the removal of the con- 
sequent to the removal of the antecedent. That is, a 
dilemma is an argument in the modus tollens of hypo- 
thetical syllogisms, as logicians love to speak. Hence 
it is plain, that if the antecedent of the major is an af- 
firmative proposition, the conclusion of the dilemma 
will be negative ; but if it is a negative proposition, the 
conclusion will be affirmative. I cannot dismiss the 
subject without observing, that as there is something 
Tery curious and entertaining in the structure of a di- 
lemma, so is it a manner or reasoning that occurs fre- 
quently in mathematical demonstrations. Nothing is 
more common with Euclid, when about ^v show the 
equality of two given figures, or, which is the same 
thing, to prove the absurdity of asserting them unequal ; 
nothing, I say, is more common with him, than to as- 
sume, that if the one is not equal to the other, it must be 
either greater or less ; and having destroyed both these 
suppositions, upon which alone the assertion can stand, 
he thence very naturally infers, that the assertion itself 
is false. Now this is precisely the reasoning of a di- 
lemma, and in every step coincides with the frame and 
composition of that argument, as we have described it 
above. 



1^6 ELEMENTS OF LOGIC. 

CHAP. V. 

©F DEMONSTRATION. 



Sec. I.... Of Reasoning hy a Concatenation of Syllogmn?. 
Having dispatched what seemed necessary to be 
said with regard to the forms of syllogisms, we now 
pjdceed to supply their use and application in reason- 
ing. We have seen that in all the different appearan- 
ces they put on, we still arrive at a just and legitimate 
conclusion. Now it often happens, that the conclusion 
of one syllogism becomes a previous proposition in 
another, by which means great numbers of them are 
sometimes linked together in a series, and truths are 
made to follow one another in train. And as in such a 
concatenation of syllogisms, all the various ways of 
reasoning that are truly conclusive, may be with safety 
introduced ; hence it is plain that in deducing any truth 
from its first principles, especially when it lies at a con- 
siderable disi?\hce from them, we are at liberty to com- 
l-ine all the several kinds of arguments above explain- 
ed, according as they are found best to suit the end and 
purpose of our inquiries. Wlien a proposition is thus, 
by means of syllogisms, collected from others more evi- 
dent and known, it is said to be _??rt)T'ec^ ; so that we 
ma}' in the general define the proof of a proposition^ 
to be a syllogism or series of syllogisms, collecting that 
proposition from known and evident truths. But more 
particularly, if the sj^llogisms of which the proof con- 
sists, admit of no premises but definitions, self-evident 
truths, and propositions already established, then is 
the argument so constituted called a demonstration; 
whereby it appears that dem.onstrations are ultimately 
founded on definitions and self-evident propositions. 

Sec. II... .All Syllogisms ■whatsoever Reducible to the first 
Figure, 
But as a demonstration oft-times consists of a long 



ELEMENTS OF LOGIC. 167 

chain of proofs, where all the various ways of arguing- 
have place, and where the ground of evidence must of 
course be different in different parts, agreeably to the 
form of the argument made use of ; it may not per- 
haps be unacceptable, if we her*; endeavour to reduce 
the evidence of demonstration to one simple principle, 
whence, as a sure and unalterable foundation, the cer- 
tainty of it may in all cases be derived. In order to 
this we must first observe, that all syllogisms whatso- 
ever, whether compound, multiform, or defective, are 
reducible to plain simple syllogisms in some one of the 
four figures. But this is not all. Syllogisms of the 
first figure in particular admit of all possible conclu- 
sions : that is, any proposition whatsoever, whether an 
universal affirmative, or universal negative, a particu- 
lar affirmative or particular negative, (which fourfold 
dirision, as we have already demonstrated in the second 
part, embraces all their varieties) any one, I say, of 
these may be inferred, by virtue of some syllogism in 
the first figure. By this means it happens, that the syl- 
logisms of all the other figures are reducible also to 
syllogisms of the first figure, and may be considered as 
standing on the same foundation with them. We cannot 
here demonstrate and explain the manner of this >re- 
^iuction, because it would too much swell the bulk of 
■'.his treatise. It is enough to take notice, that the 
thing is universally known and allowed among logi- 
cians, to whose writings we refer such as desire farther 
satisfaction in this matter. This then being laid down, 
it is plain, that any demonstration whatsoever may be 
considered as composed of a series of syllogisms, all in 
the first figure. For since all the syllogisms, that en- 
ter the demonstration, are reduced to syllogisms of some 
one of the four figures, and since the sjdlogisms of 
all the other figures are farther reducible to syllogisms 
of the first figure, it is evident, that the whole demon- 
^.tratioR may be resolved into a series of these last syl- 
logisms. Let us now, if possible, discover the ground 
jpon which the conclusion rests, in syllogisms of the 
:irst figure ; because, by so doing, we shall come at an 
I'niversai principle cf ceilainty, whence the evidence 



1GB ELEMENTS OF LOiflC. 

of all defadonstrations, in all their parts, may be ulli- 
mately derived. 

Seq. in. ...The ground of Reasoning in the first Figure, 

The rules then of the first figure are briefly these. 
The middle term is the subject of the major proposi- 
tion, and the predicate of the minor. The major is al- 
ways an universal proposition, and the minor always 
affirmative. Let us now see what effect these rules 
wiii have in reasoning. The major is an universal pro- 
position, of which the mic/cZ/e ilerm is the subject, and 
the predicate of the conclusion the predicate. Hence 
it appears, that in the major ^ the predicate of the con- 
clusion is always affirmed or denied universally of the 
middle term. Again, the minor is an affirmative pro- 
position, whereof the subject of the conclusion is the sub- 
ject, and the middle term the predicate. Here then 
the middle term is affirmed of the subject of the con- 
clusion : that is, the subject of the conclusion is affirmed 
to be comprehended under, or to make a part of the mid- 
dle term. Thus then we see Avhat is done in the premi- 
zes of a syllogism of the first figure. The predicate of 
the conclusion is universally affirmed or denied of some 
idea. The subject of the conclusion is affirmed to be, or 
to make a part of that idea. Hence it naturally and una- 
voidably follows, that the predicate of the conclusion 
ought to be affirmed or denied of the subject. To 
illustrate this by an example, we shall resume one of 
the syllogisms of the first chapter : 

Every creature possessed of Teason and liberty is accountable for his ac- 
tions. 
Man is a creature possessed of reason and liberty. 
Therefore man is accountable for his actions. 

Here, in the first proposition, the predicate of the 
conclusion, accountableness, is affirmed of all creatures 
that have reason and liberty. Again, in the second 
proposition, man, the subject of the conclusion, is af- 
firmed to be, or to make a part of this class of creatures. 
Hence the conclusion necessarily and unavoidably fol- 
lows, viz. that man is accountable for his actions. I say 
this follows necessarily and unavoidably. Because, if 
reason and liberty be that which constitutes a creature 



ELEMENTS OF LOGIC. t69 

accountable, and man has reason and liberty, it is plain 
he has that which constitutes him accountable. In like 
manner, where the major is a negative proposition, or 
denies the predicate of the conclusion universally of the 
middle term ; as the minor always asserts the subject of 
the conclusion to be or make a part of that middle term, 
it is no less evident, that ttje predicate of the conclusion 
ought in this case to be denied of the subject. So that 
the ground of reasoning, .in all syllogisms of the first 
figure, is manifestly this : Whatever may be affirmed 
univers3.lly of any idea, may be affirmed of every or any 
number of particulars comprehended under that idea. 
And •ag^^in : Whatever may be denied universally of any 
idea, may be in like manner denied of every or any 
number of its individuals. These two propositions are 
called by logicians the dictum de ojnni, and dictum de 
nullo, and are indeed the great principles of syllogistic 
reasoning ; inasmuch as all conclusions whatsoever, 
either rest immediately upon them, or upon proposi- 
tions deduced from them. But what adds greatly to 
their value is, that they are really self-evident truths, 
and such as we cannot gainsay, without running into an 
express contradiction. To affirm, for instance, that no 
man is perfect, and yet argue that some men ctre perfect ; 
er to say that all men are mortal, and yet that some men 
are not mortal, is to assert a thing to be and not to be a;t 
the same time. 

Sec. IV Demonstration, an Infallible Guide to Truth 

and Certainty. 

And now I think we are sufficiently authorized to 
affirm, that in all syllogisms of the first figure, if the 
jjremises are true, the conclusion must needs be true. 
If it be true that the predicate of the conclusion, whe- 
ther affirmative or negative, agrees universally to some 
idea... .and if it be also true, that the subject of the 
conclusion is a part of or comprehended under that idea, 
then it njcessariiy follows, that the predicate of the 
conclusion agrees also to the subject. For to assert the 
contrary, would be to run counter to some one oi the 
two principles before established ; that iz, it would be 
P 



170 ELEMENTS OF LOGIC. 

to maintain an evident contradiction. And thus we 
are come at last to the point we have been all along' en- 
deavouring to establish ; namely, that every proposi- 
tion, which can be demonstrated is necessarily true. 
For as every demonstration may be resolved into a se- 
ries of syllogisms, all in the first figure, and as in any 
one of these syllogisms, if the premises are true, the 
conclusion must needs be so too : it evidently follows, 
that if all the several premises are true, all the several 
conclusions are so, and consequently the conclusion al- 
so of the last syllogism, which is always the proposition 
to be demonstrated. Now that all the premises of a 
demonstration are true, will easily appear, from the ve- 
ly nature and definition of that form of reasoning. A 
demonstration, as we have said, is a series of syllogisms, 
all whose premises are either definitions, self-evident 
truths, or propositions already established. Definitions 
are identical propositions, wherein we connect th^ de- 
scription of an idea with the name by which we choose 
to, have that idea called; and therefi:)re ns to their 
truth there can be no dispute. Self-evident proposi- 
tions appear true of themselves, and leave no doubt or 
uncertainty in the mind. Propositions before esta- 
blished, are no other than coiiclusions, gained by one 
or more steps from definitions and self-evident princi- 
ples ; that is, from true premises, and therefore must 
needs be true. Whence all the previous propositions 
of a demonstration, being, we see, manifestly true, the 
last conclusion, or proposition to be demonstrated, must 
be so too. So that demonstration not only leads to cer- 
" tain truth,, but we have here a clear view of the ground 
and foundation ofthat certainty. For as in demonstrat- 
ing, we ma;/ be said to do nothing more than combine 
a series of syllogisms -together, all resting on the same 
l}Ottom ; it is plain, that one uniform ground of cer- 
tainty runs thrc ugh the whole, and that the conclusions 
are every where built upon some one of the two prin- 
ciples before established, as the foundation of ail our 
reasoning. These two principles are easily reduced in- 
to one, and maybe expressed thus : Whatever predicate^ 
■whether affirmative or negative, agrees imiversnJJy to 



ELEMENTS OF LOGIC. 171 

any idea, the same must needs agree to every or any 
number of individuals comprehended under that idea. 
And thus at lengtli we have, according to our first de- 
sign, reduced the certainty of demonstration to one sim- 
ple and universal principle which carries its own evi- 
dence along with it and which is, indeed, the ultimate 
foundation of all syllogistic reasoning. 

Sec. v. ...The rides of Logic furnish a sufficient criterion 
for the distinguishing between Truth and Falsehood. 

Demonstration, therefore, sending as an infallible 
guide to truth, and standing on so sure and unaltera- 
!)le a basis, we may now venture to assert, what 1 doubt 
not will appear a paradox lo .many; namely, that 
the rules of logic furnish a sufficient criterion for the 
distinguishing between truth and falsehood. For since 
every proposition that can he demonstrated is necessa- 
rily true, he is able to distinguish truth from false- 
hood, who can with certainty judge when a proposition 
is duly demonstrated. Now a dem.onstration is, as we 
have said, nothing more than a concatenation of syl- 
logisms, all whose premises are definitions, self-evi- 
dent truths, or propositions previously established. 
To judge, therefore, of the validity of a demonstration, 
we must be able to distinguish whether the definitions 
that enter it are genuine, and truly descriptive of the 
ideas they are meant to exhibit : whether the proposi- 
tions assumed without proof as intuitive truths, have 
really' that self-evidence to which they lay claim; 
'whetherthe syllogisms are draivn up in due form, and 
agreeable to the laws of argumentation ; in fine, v/he- 
ther they are combined together in a just and orderly 
manner, so that no demonstrable propositions serve any 
where as premises, unless the}^ arc conclusions of pre- 
vious syllogisms. Now it is the business of logic, in 
explaining the several operations of the mind, fully to 
instruct us in all these points. It teaches the nature 
and end of definitions, and lays down the rules by which 
they ought to be framed. It unfolds the several spe- 
cies of propositions, and distinguishes the self-evident 
from the dem.onstrable. It delineates also the differ- 



1/2 ELEMENTS OF LQGlC. 

cnt forms of syllogismS) and explains th« laws of argU" 
nientation proper to each. In fine, it describes the 
manner of combining syllogisms, so as that they may 
form a train of reasoning, and lead to the successive 
discovery of truth* The precepts of logic, therefore. 
as they enable us to judge with certainty, Avhen a pro- 
position is duly demonstrated, furnish a sure criterion 
for distinguishing between truth and falsehood. 

Sec» VI..,, And extending to all Cases where a certain 
Knowledge of Truth is attainable. 

But perhaps it maybe objected, that demonstratioB 
is a thing very rare and uncommon, as being the pre- 
rogative of but a few sciences, and therefore the crite- 
rion here given can be of no great use. I answer, that 
wherever by the bare contemplation of our ideas, truth 
is discoverable, there also demonstration may be ob- 
tained. Now that I think is an abundantly sufficient 
criterion, which enables us to judge with certainty, 
in all cases where the knowledge of truth comes with- 
in our reach ; for with discoveries that lie beyond the 
limits of the human mind we have properly no business 
nor concernment. When a proposition is demonstra- 
ted, we are certain of its truth. When on the con- 
trary, our ideas are such as have no visible connexion 
nor repugnance, and therefore furnish not the proper 
means of tracing thejr agreement or disagreement, 
there we are sure that knowledge, scientifical know^- 
ledge I mean, is not attainable. But where there is 
some foundation of reasoning, which yet amounts not 
to the full evidence of demonstration, there the pre- 
cepts of logic, by teaching us to determine aright of 
the degree of proof, and of what is still wanting to 
render it full and complete, enable us to make a due 
estimate of the measures of probability, and to propor- 
tion our assent to the grounds on which the proposi- 
tion stands. And this is all we can possibly arrive at, 
©r even so much as hope for, in the exercise of facul- 
ties so imperfect and limited as ours. For it were 
the height of folly, to expect a criterion that should 
enable us to distinguish truth from falsehood, m 



ELEMENTS OF LOGIC. 173 

casies where a certain knowledge of truth is not at 
tainable. 

Sec. vir The Distinction of Demonstration into di- 
rect and indirect. 

We have now done with what regards the ground 
and evidence of demonstration ; but before we con- 
clude this chapter, it may not be improper to take no- 
tice of the distinction of it into direct and indirect. 
A direct demonstration is, when beginning with defi- 
nitions, self-evident propositions, or known and allow- 
ed truths, we form a train of syllogisms, and combine 
them in an orderly manner, continuing the series 
through a variety of successive steps, until at last we 
arrive at a syllogism, whose conclusion is the pmposi- 
tion to be demonstrated. Proofs of this kind leave no 
doubt or uncertainty behind them ; because all the se- 
veral premises being true, the conclusions must bes©. 
too, and of course the very last conclusion, or proposi- 
tion to be proved. I shall not, therefore, any farther, 
enlarge upon this method of demonstrating ; having, I 
hope, sufficiently explained it in the foregoing part of 
this chapter, and shown wherein the force and validit}- 
of it lies. The other species of demonstration is the 
indirect, or, as it is sometimes called, the apologicaL 
The manner of proceeding here is, by assuming a pro- 
position which directly contradicts that we mean ta 
demonstrate, and thence by a continued train of rea- 
soning, in the way of a direct demonstration, deducing- 
some absurdity or manifest untruth. For hereupon 
we conclude that the proposition assumed was false, 
and thence again, by an immediate consequence, that 
the proposition to be demonstrated is true. Thus Eu- 
clid, in his third book, being to demonstrate, that cir- 
cles which touch one another inzvardly have not the 
same centre ; assumes the direct contrary to this, viz. 
that they have the same centre ; and hence by an evi- 
dent train of reasoning, proves, that a part is equal to 
the -vchole. The supposition therefore leading to the 
absurdity he concludes to be false, viz. that circles 
touching one another inwardly have the sa?ne ceiitre^ 
P^ 



174' e;lements of logic. 

and thence again immediately infers, that they have not 
the same centime. 

Se€. VIII Ground of B.eai,oning in indirect DemQn- 

strations. 
Now because this manner of demonstration is ac- 
counted by some not altogether so clear and satisfac- 
tory nor to come up to that full degree of evidence, 
which we meet with in the direct way of proof ; I 
shall, therefore, endeavour here to give a pal-ticular il- 
lustration of it, and to show that it equally with the 
other leads to truth and certainty. In order to this 
we must observe, that two propos^ions are said to be 
£07i^ra<iic/;or7/ one of another, when that which is as- 
serted to be in the one, is asserted not to be in the 
other. Thus the propositions — circles that touch one 
another inwardly have the same cenVie — and circles that 
touch one another inzvardly have not the same centre — 
are, contradictories ; because the second asserts the di- 
rect contrary of what is asserted in the first. Now in 
ill! contradictory propositions, this holds universally, 
that one of them is necessarily true, and the other ne- 
cessarily false. For if it be true, that circles, which 
touch one another inwardly, have not the same centre, 
it is unavoidably false, that they have the same centre. 
On the other hand, if it be false that they have the 
same centre, it is necessarily true, that they have not 
the same centre. Since therefore, it is impossible for 
them to be both true or both false at the same time, 
it unavoidably follows, that one is necessarily true, and 
the other necessarily false. Tbis then being allowed, 
which is indeed self-evident, if any two contradictory 
propositions are assumed, and one of them can by a 
clear train of reasoning be demonstrated to be false, 
it necessarily follows that the other is true. For as 
the one is necessarily true, and the other necessarily 
false, when we come to discover which is the fa^se pro- 
position, we thereby also know the other to be true. 

Sec. IX Indirect Demonstr aliens a sure Guide to Cer- 
tainty. 
Now- this is precisely the manner of an indirect de 



ELEMENTS OP LOGIC. 175 

monstration, as is evident from the account given of ic 
above. For there we assume a proposition, vvluch di- 
rectlj^ contradicts that we mean to demonstrate, and 
having, by a continued series of proofs, shown it to be 
false, thence infer that its contradictory, or the propo- 
sition to be demonstrated, is true. As therefore this 
last conchision is certain and unavoidable, let us next 
inquire, after what manner we come to be satisfied of 
the falsehood of the assumed proposition, that so no 
possible doubt may remain, as to the force and validity. 
cf demonstrations of this kind. The manner, then, is 
plainly this. Beginning- with the assumed proposition, 
we by the help of definitions, self-evident truths, or 
propositions already established, continue a series of 
reasonin ;, in the way of a direct demonstration, until 
at length we arrive at some absurdity or known false- 
hood. Thus Euclid^ in the example before mentioned 
from the supposition that circles touching one another 
inwardly have the same centre, deduces, that a part is 
equal to the Ti'hole, Since, therefore, by a due and or- 
derly process of reasoning, we come at last to a false 
conclusion, it is manifest, that all the premises cannot be 
true. For were all the premises true, the last conclu- 
sion must be so too, by what has been before demon- 
strated. Now as to ail the other premises mide use of 
in the course of reasoning, they are manifest and 
known truths by supposition, as being either definitions, 
self-evident propositions, or truths established. The 
assumed proposition is that only as to which any doubt 
or uncertainty remains. That alone, therefore, can 
be false, and indeed, from what has been already shown, 
must unavoidably be so. And thus we see, that in in- 
direct demonstratiohs, two contradictory propositions 
being laid down, one of which is demonstrated to be 
false, the other, which is always the proposition to be 
proved, must necessarily be true ; so that here, as well 
as in the direct way of proof, we arrive at a clear and 
satisfactory knowledge of truth. 

Sec. x....v'1 particular Case of Indirect demonstration. 

This is universally the method of reasoning in all 



178 . ELEIMENTS OF LOGIC. 

apologicai or indirect demonstrations ; but there is one 
particular case, which has something so singular and 
curious in it, that well deserves to be mentioned by it- 
self ; more especially, as the ground on which the con- 
clusion rests will require some farther illustration. It 
is, in short, this : that if any proposition is assumed,, 
from which in a direct train of reasoning we can deduce 
its contradictory, the proposition so assumed is false, 
and the contradictory one true. For if we suppose the 
assumed proposition to be true, then since, all the other 
premises that enter the demonstration are also true, we 
shall have a series of reasoning, consisting wholly of 
true premises ; whence the last conclusion, or contra- 
dictory of the assumed proposition, must be true like- 
wise. So that by this means we should have two con- 
tradictory propositions both true at the same time, 
which is manifestly impossible. The assumed proposi- 
tion, therefore, whence this absurdity flows, must ne- 
cessarily be false, and consequently its contradictory, 
which is here the proposition deduced from it must be 
true. If then any proposition is proposed to be demon- 
strated, and we assume the contradictory of that pro- 
position, and thence directly infer the proposition to he 
demonstrated by this very means we know that the 
proposition so inferred is true. For since from an as- 
sumed proposition we have deduced its contradictory, 
we are thereby certain that the assumed proposition is 
false; and if so, then its contradictory, or that deduc- 
ed from it, which in this case is the same with the pro- 
position to be demonstrated, must be true. 

Sec. XI... .a due Knowledge of the Principles of Logic 
indispensably necessary to make us proper judges of 
Demonstration ; 

That this is not a mere empty speculation, void of 
all use and application in practice, is evident from the 
conduct of the mathematicians, who have adopted this 
manner of reasoning, and given it a place among their 
demonstrations. We have a curious instance of it in 
the twelfth proposition of the ninth book of the ele- 
ments, Euclid there proposes to demonstrate that m 



ELEMENTS OF LOGIC. 177 

uny series of numbers, arising from unity in geometrical 
progression, all the prime numbers, that measure the last 
term in the series, will also measure the next after unity. 
In order to this he assumes the contradictory of the pro- 
position to be demonstrated, namely ; that some prime 
number measuring the last term in the series, does not 
measure the next after unity, and thence by a continued 
train of reasoning proves, that it actually does measure 
ii. Hereupon he concludes the assumed proposition to 
be false, and that which is deduced from it, or its con- 
tradictory, which is the very proposition he proposed 
to demonstrate, to be true. Now that this is a just 
nnd conclusive way of reasoning, is abundantly mani- 
fest, from what we have so clearly established above, 
I would only here observe, how necessary some know- 
ledge of the iTiles of logic is, to enable us to judge of 
the force, justness, and validity of demonstrations ; 
since such may sometimes occur, where the truth of the 
proposition demonstrated will neither be owned nor 
perceived, unless we know. before-hand, by means of 
logic, that a conclusion so deduced, is necessarily true 
and valid. For though it be readily allowed, that by 
the mere J>trength of our natural faculties, we can at 
once discern, that of two contradictory propositions, 
the one is necessarily true, and the other necessarily 
false : yet when they are so linked together in a demon- 
stration, as that the one serves as a previous proposition, 
whence the other is deduced ; it does npt so immediate- 
ly appear, without some knowledge of the principles of 
logic, why that alone, which is collected by reasoning, 
ought to be embraced as true, and the other, whence it 
is collected, to be rejected as false. 

Sec. xii.,,. And of itself sufficient to guard us against 
Error and false Reasoning. 

Having thus, 1 hope, sufficiently evinced the certain- 
ty of demonstration in rH its branches, and shown the 
rules by which we ought to proceed, in order to arrive 
at a just conclusion, according to the various ways of 
arguing made use of; I hold it needless to enter upon 
a particular consideration of those several species ot 



178 ELEMENTS OF LOGIC, 

false reasoning which logicians distinguish by the name 
of sophisms,. He that thorough!}^ understands the form 
and structure of a good argument, will of himself read- 
ily discern every deviation from it. And although so- 
fhisms have been divided into many classes, which are 
all called by sounding names, that therefore carry in 
them much appearance of learning ; yet are the errors 
themselves so xerj palpable and obvious, that I should 
think it lost labour to write for a man capable of beirig 
misled by them. Here, therefore, we choose to con- 
clude this third part of logic, and shall in the next bodk 
give some account of we^/iocZ, which, though insepara- 
ble from reasoning, is nevertheless alwa,ys considered 
by logicians as a distinct operation of the mind ; be- 
cause its influence is not confined to the mere exercise 
of the reasoning faculty, but extends in some degree to 
all the transactions of the understanding. 



BOOK lY. 

Of Method, 

CHAP. I. 

AF JIETHCD m GENERAL, AND THE DIVISION OP IT 
INTO ANALYTIC AND SYNTHETIC. 






Sec, i...,The understanding sometimes employed input- 
ting together known truths. 

Vi-^E have now done with the three first operations 
«f the mind, whose office it is to search after truth, 
and enlarge the bounds of human knowledge. There 
is yet a fourth, which regards the disposal and arrange- 
ment of our thoughts, when we endeavour so to put them 
.together, that their mutual connexion and dependence 



ELEMENTS OF LOGIC* 179 

may be clearly seen* This is what logicians cnll ms- 
thody and place always the last in order, in explaining' 
the powers of the understanding-; because it necessa- 
ril}^ supposes a previous exe^xise of our other faculties, 
and some progress made in knowledge, before we can 
exert it in any extensive degree, ft often happens, in 
the pursuit of truth, that unexpected discoveries pre- 
sent themselves to the mind, and those, too, relating to 
subjects very remote from that about which we are at 
present emploj'ed. Even the subjects themselves of 
our inquiry, are not always chosen with a due regard 
to . order, and their dependence one upon another. 
Chance, our particular way of life, or some present and 
pressing views, often prompt us to a variety of research- 
es, that have but little connexion in the nature of things. 
W'.en, therefore, a man accustomed to much thinlir.'ng, 
comes, after any considerable inter/al of time, to take 
a survey of his in{cllectu;i' acquisitions, he seldom finds 
reason to be satisfied with that order and disposition, 
according to which they made their entrance into his 
understanding. They are there dispersed and scatter- 
ed, without subordination, or any just and regular co- 
herence ; insomuch that the subserviency of one truth 
to the discovery of another, does not so readily appear 
to the mind. Hence he is convinced of the necessity 
of distributing them into various classes, and combining 
into an uniform system whatever relates to one and the 
same subject. Now this is the true and proper business 
of method; to ascertain the various divisions of humarr 
knowledge, and so to adjust and connect the parts in 
every branch, that they may seem to grow one out of 
another, and form a regular body of science, rising 
frmn first principles, and proceeding by an orderly con- 
catenation of truths. 

Sec. II Sometitnesm the Search and Discovery of such 

as are unknown. 

In this view of thiiigs, it is plain, that we must be be- 
fore-hand well acquainted with the truths we are to 
combine together ; otherwise hc.^^ could we discewi 



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no: 


tnem 


v-^ 


to p 


i?S, 


that 


>--e- 


e ■? . 


: ^ ■•. 


inJed 


ad 


(■•■Ill 


-V 


::^ J 


he 


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i?i- 







180 ELEMENTS OF LOGIC. . 

their several connexions and relations, or so dispose of 
them as their mutual dependence may require ? But 
BOW it often happens, the understanding is employed, 
not in the arrangement and composition of known 
truths, but in the search and discovery of such as are 
unknown. And here the manner of proceeding is very 
different, inasmuch as we assemble at once our whole 
stock of knowledge relating to any subject, and, after 
a general survey of things, begin with 
separately and by parts. Hence it cc 
whereas at our first setting out, we 
only with some of the grand strokes , 
may so say, of truth by thus pursn^n?- 
several windings and recesses, we 27 
those more inward and finer touches, whe^ 
rives all her strength, symm'^try and be : i 

liere it is, that when by a narrow scruti*] g's, 

we have unravelled any part of know I: v^ :.v:ed 

it to its first and original principles, in^- o *hat the 
whole frame and contexture of it m^s •: :o the view 

of the niind ; here, I say, it is, tV.rnc , -i the con- 

trary way, and beginning with th. -..iples, we can 

so adjust and put together tht^ ' , as the order and 
method of science requires. 

Sec. III..,. Illustrated oy the Similitude of a Watch. 

But as these things are best understo :" when i-lus- 
trated by examples, especially if they arc obvious, i nd 
taken from common life ; let us suppose any machine, 
for instance, a watch, presented to us, whose structure 
and composition we are as yet, unacquainted with, but 
v/ant, if possible, to discover. The manner of pro- 
ceeding, in this case, is, by taking the whole to pieces, 
and examining the parts separately one after another. 
When by such a scrutiny we have thoroughly inform- 
ed ourselves of the frame and contexture of each, wc 
then compare them together, in order to judge of their 
mutual action and influence. By this means we gra- 
dually trace out the inward make and composition of 
the whole, and come at length to discern, how parts of 
such a form,, and so put togeiher as we found, in unra- 



ELEMENTS OF LOGIC. 181 

veiling aud takinp: them asunder, constitute that par- 
ticular machine called a watch, and contribute to all 
the several motions and phenomena observable in it. 
This discovery being made, we can take things the con- 
trary way, andj beginning with the parts, so dispose 
and connect them, as their several uses and structures 
require, until at length we arrive at the wifole itself, 
from the unravelling of which these parts resulted. 

Sec. IV.... Ground of the Analytic and Synthetic me- 
thods. 

And as it is in tracing and examining the works of 
art, so it is in a great measure in unfolding any part of 
human knowledge. For the relations and mutual ha- 
bitudes of things, do. not always iijgmediate]}'" appear, 
upon comparing them one with another. Hence we 
have recourse to intermediate ideas, and, by means of 
ihem, are furnished with those previous propositions 
that lead to the conclusion we are in quest of. And if 
it so happen, that the previous propositions themselves 
arc not sufficiently evident, we endeavour, by new 
middle terms, to ascertain their truth, still tracing 
things backward in a continued series, until at length 
we arrive at some S3'llogism, where the premises arc 
first and self-evident principles. This done , we become 
pertectly satisfied as to the truth of all the conclusions 
wehavepasaed through, inasmuch as they are now seen 
to stand upon the firm and immovable foundation of our 
intuitive perceptions. And as we arrived at this cer- 
laintyi by tracing things backward to the original prin- 
ciples whence they flow, so may we at any time renew 
it by a direct conlrary process, if beginning with these 
principle:*, v,e carry the train of our thoughts forward- 
until they lead us by a connected chain of proofs, to 
the very last conclusion of the series. 

Sec. V. ...Division of Method into Analytic and Syn- 
a, thetic. 
Hence it appears, that in disposing and putting to- 
gretherour thoughts, either for our own use, that the 
discov'eries we have made may at all times lie open to 
tHe review of the mind ; or, where we mean to com- 

Q 



182 ELEMENTS OF LOGIO. 

municate and unfold these discoveries to others, there 
are two ways of proceeding, equally within our choice. 
For we may so propose the truths relating to any part 
of knowledge, as they presented themselves to the mind 
in the manner of investigation, carrying on the series 
of proofs in a reverse order, until they at last terminate 
in first principles : or, beginning with theseprinciples^ 
we take the contrary way, and from them deduce, 
by a direct train of reasoning, all the several proposi- 
tions we want to establish. This diversity in the 
manner of arranging our thoughts gives rise to the 
twofold division of method established among logi- 
cians. For method, according to their use of the word, 
is nothing else bi4 the order and disposition of our 
thoughts relating to any subject. When truths are so 
proposed and put together, as they were or might have 
been discovered, this is called the analytic method, or 
the method of resolution ; inasmuch as it traces things 
backward to their source, ?iY\di resolves knovrledge into 
its first and original principle. When on the other 
hand, they are deduced from these principles, and con- 
nected according to their mutual dependence, inso- 
Kiuch that the truths first in order tend always to the 
demonstration of those that follow, this constitutes 
what we call the synthetic method, or method of compo- 
sition. For here we proceed by gatherijig together 
several scattered parts of knowledge, and combining 
them into one whole, or system, in such manner, that 
the understanding is enabled distinctly to follow truth 
through all her different stages and gradations. 

Sec. Yi... .Called oiJio^wise the Method of Invention 
and the Method cf Science. 

There is farther to be taken notice of, in relation 
to these two species of method ; that the first has also 
obtained the name of the method of invention, because 
it observes the order in which our thoughts succeed one 
another, in the invention or discovery of truth. The 
other, again, is often denominated the method of doc- 
trine, or instruction, inasmuch as in laying our thoughts 
before others, we generally choose to proceed in the 



ELEMENTS OF LOGIC. 183 

s-ynthetic manner, deducin^^ them from their first prin- 
ciples. For we are to observe, that although there is 
great pleasure in pursuing truth in the method of inves- 
tigation, because it places us in the condition of the 
inventor, and shows the particular train and process of 
thinking by which he arrived at his discoveries ; yet it 
is not so well accommodated to the purpose of evi- 
dence and conviction. For at our first setting out, we 
are commonly unable to divin5 where the analj^sis will 
lead us ; inasmuch that our researches are for some 
time little better than a mere groping in the dark. 
And even after light begins to break in upon us, we arc 
still obliged to many reviews, and a frequent compari- 
son of the several steps of the investigation among 
themselves. Nay when we have unravelled the whole, 
and reached the very foundation on which our discove- 
ries stand, all our certainty, in regard to their truth, 
will be found in a great m ea^ure to arise from that 
connexion we are now able to discern between them 
and first principles, taken in the order of composition. 
But in the synthetic manner of disposing our thoughts, 
the case is quite different. For as we here begin with 
intuitive truths, and advance by regular deductions 
from them, every step of the procedure brings evidence 
and conviction along with it ; so that in our progress 
from one part of knoAvledge to anotl^er, we have al- 
ways a clear perception of the grounds on which our a3> 
sent rests. In communicating therefore, our discove- 
ries to others, this method is apparently to be chosen, 
as it wonderfully improves and enlightens the under- 
standing, ajid leads to an immediate perception of truth- 
And hence it is, that in the following pages, we choose 
to distinguish it by the name of Ihe method of science ; 
not only as in the use of it we arrive at science and cei- 
tainty, but because it is in fact the method, in which 
all those parts of human knowledge, that properly bear 
the name of science, are and ought to be delivered. 
But we now proceed to explain these two kinds of me- 
thod more particularly. 



i84 ELEMENTS OF LOGIC, 

CHAP. II. 

OF, THE METHOD OF INVENTION. 

>^EC. I, ...Origin of the several Arts and Inventiom 
of Human Life . 

By the method of invention we understand such a 
disposition and arrangement of our thoughts, as follows 
the natural procedure of the understanding, and pre- 
sents them in the order in which they succeed one, 
f^nother, in the investigation and discovery of truth. 
Now it is plain, that to handle a subject successfully 
according to this method, we have no more to do than 
observe the several steps and advances of our minds, 
and fairly copy them out to the view of others. And 
indeed it will be found to hold in general, with regard 
to all the active parts of human life, especially when 
reduced to that which is in the schools termed an art ; 
that the rules bj^ which we conduct ourselves, are n® 
other than a series of observations drawn from the at- 
tention of the mind to what passes, while we exercise 
our faculties in that particular way. For when we set 
about any invention or discovery, we are always push- 
ed on by some inward principle, disposition, or aptitude 
shall I call it, which we experience in ourselves, and 
which makes us believe, that the thing we are in quest 
of, is not altogether beyond our reach. We therefore 
begin Avith essaying our strength, and are sometimes 
successful, though perhaps more frequently not. But 
as the mind, when earnestly bent upon any pursuit, is 
not easily discouraged by a few disappointments, we are 
only set upon renewing our endeavours, and by an ob- 
stinate perseverance, and repeated trials, often arrive 
at the discovery of what we have in view. Now it is 
natural for a man of a curious and inquisitive turn, af- 
ter having mastered any part of knowledge with great 
labour and diiiiculty, to set himself to examine how he 
happened to miscarry in his first attempts, and by what 
particular method of procedure he at length came to be 



ELEMENTS OF LOGIC. 185 

successful. By this means we discover on the one 
hand, those rocks and shelves which stand most in our 
way, and are apt to disturb and check our progress ; and 
on the other, that more sure and certain course, which 
if we continue in steadily, will bring us to the attain- 
ment of what we are in pursuit of. Hence spring all 
the arts and inventions of human -life, which, as we 
have already said, are founded upon a series of rules and 
observations, pointing out the true and genuine manner 
of arriving at any attainment. When the mind rests 
satisfied in a bare contemplation of the rules, and the 
reasons on which they are founded, this kind of know- 
ledge is called speculative. But if we proceed farther, 
and endeavour to apply these rules to practice, so as to 
acquire a habit of exerting them on all proper occa- 
sions, we are then said to be possessed of the art itself. 

Sec. II. ...Why in treating of the Method of Invention^ 
we must give som&4iccount of the Art itself 

From what has been said, it appears, that, in order 
distinctly to explain the method of invention, we must 
take a view of the understanding, as employed in the 
search and investigation of truth. For by duly attend- 
ing to its procedure and advances, u-e shall not only 
discover the rules by which it conducts itself, but be 
enabled also to trace out the several helps and contri- 
vances it makes use of, for the more speedy and effect- 
ual attainment of its ends. And when these particulars/ 
are once known, it will not be difficult for us, in laying 
open our discoveries to others, to combine our thoughts 
agreeably to the method here required. Because, hav- 
ing fixed and ascertained the rules of it, and being per- 
fectly acquainted with the conduct and manner of the 
mind, we need only take a view of the several truths, 
as they succeed one another in the series of investiga- 
tion, set them in order before us, and fairly transcribe 
the appearance they make to the understanding. Hence 
it is, that logicians, in treating of the method of in-. 
vention, have not merely confined themselves to the 
laying down of directions for the disposal and arrange- 
ment of our thoughts : but have rather cxplai/ied ihs 
^.2 



3 86 ELEMENTS OF LOGIC. 

art itself, and established those rules by which tlie mind 
ought to proceed in the exercise of its inventive power?. 
For they rightly judge, that if these were thoroughly 
understood, the other could no longer remain unknown. 
By this means it happens, that the method of invention 
is become another expression for the art of invention^ 
and very often denotes the conduct and procedure of the 
understanding in the search of truth. And as some 
knowledge of the principles of the art, is in a manner 
absolutely necessary towards a true conception of the 
rules by which we ought to govern and dispose our 
thoughts in treating subjects after this method ; we 
shall, therefore, follow the example of other logicians, 
and endeavour to give some short account of the busi- 
ness of invention, and of those several helps and con- 
trivances by which the mind is enabled to facilitate and 
enlarge its discoveries. 

Sec. III.... Attention and a comprehensive understanding 
the preparatory qualijications to Invention. 

It has been already observed, that when the mind 
employs itself in the search of unknown truths, it be- 
gins with assembling at once its whole stock of know- 
legde relating to the subject, and after a general sur- 
vey of things, sets about examining them separately 
and by parts. Now as in this separate examination, 
the number of parts continually increase upon us — and 
as it is farther necessary, that we survey them on all 
sides, compare them one with another, and accurately 
trace their mutual habitudes and respects — it is from 
hence apparent, that in the exercise of invention, two 
Ihings are of principal consideration. First, an en- 
larged and comprehensive understanding, able to take 
in the great multitude of particulars, that frequently 
come under our notice. Secondly, a strong habit of 
attention, that iets. nothing remarkable slip its view, 
and distinguishes carefully all those circumstances 
which tend to the illustrating and clearing the sub- 
ject we are upon. These are the great and preparatory 
qualifications, without which it were vain to hope, that 
a»y cpnsldieRt)l§ advance could be made in e&larging 



ELEMENTS OF LOGIC. 187 

the bounds of human knowledge. Nor ought we to 
esteem it a small advantage, that they are in some mea- 
sure in our own power, and may, by a proper cultiva- 
tion, be improved and strengthened to a degree, almost 
beyond belief". We find by experience, that the study 
ef mathematics in particular is greatly serviceable to 
this end. Habits, we all know, grow stronger by ex- 
ercise ; and as in this science there is a perpetual call 
upon our attention, it by degrees becomes natural to 
us, so as that we can preserve it steadj^ and uniform, 
through long and intricate calculations, and that with 
little or no fatigue to the understanding. But a yet 
more wonderful advantage, arising from the culture of 
the mathematics, is this, that hereby we in some mea- 
sure extend the dimensions of the human mind, enlarge 
its compass of perception, and accustom it to wide and 
comprehensive views of things. For whereas at our 
first setting out, we often find it extremely difficult to 
master a short and easy demonstration, and trace the 
connexion of its several parts ; yet as we advance in 
+he science, the understanding is seen gradually to di- 
late, and stretch itself to a greater size ; insomuch that 
a long and intricate series of reasoning is often taken in 
with scarce any labour of thought ; and not only so, but 
we can in some cases, with a single glance of our minds^ 
run through an entire S3{^tem of truths, and extend our 
view at once to all the several links that unite and hold 
them together. 

Sec IV.... Judicious choice of intermediate Ideas another 
great requisite in this Art. 

When we are furnished with these two preparatory 
qualifications, the next requisite to the discovery o§ 
truth is, a judicious choice of intermediate ideas. We 
have seen in the third part of this treatise, that many 
of our ideas are of such a nature as not to discover 
these several habitudes and relations by an immediate 
comparison one with another. In this case, we must 
have recourse to intermediate ideas ; and the great art 
lies in finding out such as have an obvious and perceiv- 
able connexion with the idea? whose relations we ia- 



188 ELEMENTS OF LOGIC. 

quire after. For thus it is, that we are furnished witli 
known and evident truths, to serve as premises for the 
discovery of such as are unknown. And indeed the 
whole business of invention seems, in a great measure, 
to lie in the due assemblage and disposition of these 
preliminary truths. For they not only lead us, step 
by step, to the discovery we are in quest of, but are 
so absolutely necessary in the case, that without them 
it were vain to attempt it ; nothing being more cer- 
tain, than that unknown propositions can no otherwise 
be traced but by means of some connexion they have 
with such as are known. Nay, reason itself, which is 
indeed the art of knowledge, and the faculty by which 
we push on our discoveries ; yet by the very definition 
of it implies no more, than an ability of deducing un- 
known truths from principles or propositions that are 
already known. Now, although this happy choice of 
intermediate ideas, so as to furnish a due train of pre- 
vious propositions, that sliall lead us successively from 
one discovery to another, depends in some measure 
upon a natural sagacity and quickness of mind : it is 
yet certain, from experience, that even here much may 
be effected by a stubborn application and industry. In 
order to this, it is in the first place necessary, that we 
have an extensive knowledge of thingSj, and some gen- 
eral acquaintance with the whole circle of the arts and 
sciences. Wide and extended views add great force 
and penetration to the mind, and enlarge its capacity 
of judging. And if to this we join in the second place, 
a more particular and intimate study of whatever re- 
lates to the subject about which our inquiries are em- 
ployed, we seem to bid fair for success in our attempts* 
For thus we are provided with an ample variety out of 
which to choose our intermediate ideas, and are there- 
fore more likely to discover some among them that will 
furnish out the previous propositions necessary in any 
train of reasoning. 

Sec. v..., Sagacity and a quickness of understanding 
greatly promoted by the study of Algebra, 

It is not, indeed, to fee denied, that when we have 



ELEMENTS OF LOGIC. 109 

oven got al! our materials about us, much still depends 
upon a certain dexterity and address, in singling out 
the most proper, and applying them skilfully for the 
discovery of truth. This is the talent which is known 
by the name of sagacity, and commonlj^ supposed to 
be altogether the gift of nature. But yet I think it is 
beyond dispute, that practice, experience, and a watch- 
ful attention to the procedure of our own minds, while 
employed in the exercise of reasoning, are even here of 
very great avail. It is a truth well known to those 
who have made any considerable progress in the study 
of algebra, that an address and sliill in managing in- 
tricate questions may be very often obtained, b}^ a care- 
ful imitation of the best models. For although when we 
first set out about the solution of equations, we are puz- 
zled at every step, and think we can never enough ad- 
mire the sagacity of those who present us Avith elegant 
models in that way ; yet by degrees we ourselves ar- 
rive at a great mastery, not only in devising proper 
equations, and coupling them artfully together, so as 
from the more complicated to derive others that are 
simple ; but also in contriving useful substitutions, to 
free our calculations from fractions, and those intrica- 
cies that arise from surds and irrational quantities. Noi; 
is it a small pleasure attending the prosecution of this 
study, that we thus discern the growing strength of our 
minds, and see ourselves approaching nearer and near- 
er to that sagacity and quickness of understanding 
which we see so much admired in others, and were at 
first apt to conclude altogether beyond our reach. 

Sec. vr Where Art and Management are required in 

the business of invention. 

We have now considered those requisites to inven- 
tion, that have their foundation in the natural talents 
of the mind : an enlarged and comprehensive under- 
standing, a strong habit of attention, a sagacity and 
quickness in discerning and applying intermediate 
ideas. Let us next take a view of such other helps, as 
more immediately depend upon art and management, 
and show the address of the mind, in contriving mesons 



190 ELEMENTS OF LOGIC. 

to facilitate its discoveries, and free it from all unneces- 
sary fatig"ue and labour. For we are to observe, that 
though the capacit}^ of the intellect may be greatly en~ 
larged by use and exercise, yet still our views are con- 
fined within certain bounds, beyond which a finite un- 
derstanding cannot reach. And as it often happens, in 
the investigation of truth, especially where it lies at a 
considerable distance from first principles, that the num- 
ber of connexions and relations are so great, as not to be 
taken in at once by the most improved understanding ; 
it is therefore one great branch of the art of invention, 
to take account of these relations, as they come into 
view, and dispose them in such manner, that they al- 
ways lie open to the inspection of the mind, when dis- 
posed to turn its attention that way. By this means, 
without perplexing ourselves with two many considera- 
tions at once, we have yet these relations at command, 
when necessary to be taken notice of in the prosecution 
of our discoveries : and the understanding, thus free 
and disengaged, can bend its powers more in tensely to- 
wards that particular part of the investigation it is at 
present concerned with. Now in this, according to my 
apprehension, lies the great art of human knowledge ; 
to manage with skill the capacity of the intellect, and 
contrive such helps as may bring the most wide and ex- 
tended objects within the compass of its natural powers. 
When, therefore, the multitude of relations increase 
very fast upon us, and grow too unwieldly to be dealt 
with in the lump, we must combine them in different 
classes, and so dispose of the several parts, as that they 
may at all times lie open to the leisurely survey of the 
mind. By this means we avoid perplexity and confu- 
sion, sind are enabled to conduct our researches, with- 
out being puzzled with that infinite crowd of particu- 
lars, that frequently fall under our notice in long and' 
difficult investigations. For by carrying our attention 
successively from one part to another, we can, upon oc- 
casion, take in the whole ; and knowing also the order 
and diijposition of the parts, may have recourse to any 
of them at pleasure, when its aid becomes necessary ia 
the course q( our inquiries. 



ELEMENTS OF LOGIC. 191 

•Sec. vii.... Jin orderly disposition of great use in 
adapting objects to the capacity of (he understanding ; 

First then I say, that an orderly combination of things 
and classing them together with art and address, brings 
great and otherwisv^ unmanageable objects, upon a level 
witii the powers of the mind. We have seen, in the 
firsi prirt of this treatise, how by taking numbers in a 
progressive series, and according to an uniform law of 
composition, the most bulky and formidable collections 
are comprehended with ease, and leave distinct impres- 
sions in the understanding. For the several stages of 
the progression serve as so many steps to the mind, by 
which it ascends gradually to the highest combinations ; 
and as it can carry its views from one to another, with 
great ease and expedition, it is thence enabled to run 
over all the parts separately, and thereby rise to a just 
conception of the whole. The same thing happens in 
all our other complex notions, especially when they 
grow very large and complicated-; for then it is that 
we become sensible of the necessity of establishing a 
certain order and gradation in the manner of combining 
the parts. This has been already explained, at some 
length, in the chapter of the composition and resolu- 
tion of our ideas ; v/here we have traced the gradual 
progress of the mind through all the different orders of 
perception, and shown, that the most expeditious way 
of arriving at a just knowledge of the more compound- 
ed notices of the understanding, is by advancing regu- 
larly through -<;il the intermediate steps. Hence it is 
easy to perceive what advantages must arise from a like 
conduct in regard to those several relations and connex- 
ions, upon which the investigation of truth depends. 
For as by this means we are enabled to bring them all 
within the reach of the mind, they can each in their 
turns be made use of upon occasion, and fi>rnish their 
assistance towards the discovery of what we are in quest 
of. Now tliis is of principal consideration in the busi- 
ness of invention, to have our thoughts so much under 
comaiand, that, in comparing thitjgs together, in order 
to discover the result ot their mutual co.i' f^xions an i de- 
pendence, all the several lights that tend to the clearing 



192 ELEMENTS OF LOGIC. 

the subject we are upon, may lay distinctly open to the 
understanding, so as nothing material shall escape its 
view : because an oversight of this kind, in summing 
up the account, must not only greatly retard its advan- 
ces, but in many cases check its progress altogether. 

Sec, VIII And enahling us to proceed gradually and 

"with ease in the investigation of Truth. 

But secondly, another advantage arising from this 
orderly disposition, is, that hereby we free the mind 
from all unnecer^sarv fatigue, and leave it to fix its at- 
tention upon any part separately, without perplexing 
itself with the consideration of the whole. Unknown 
truths, as we have already observed, are only to be 
traced by means of the relation between them and others 
that are known. When, therefore, these relations be- 
come very numerous, it must needs greatly distract the 
mind, were it to have its attention continually upon the 
stretch after such a multitude of particulars at once. 
But now, by the method of classing and ordering our 
perceptions above explained, this inconvenience is 
wholly prevented. For a just distribution of things, as 
t ascertains distinctly the place of each, enables us to 
call any of them into view at pleasure, when the present 
consideration of it becomes necessary. Hence the mind 
proceeding gradually through the several relations of 
its ideas, and marking the results of them at every step, 
can always proportion its inquiries to its strength ; and 
confining itself to such a number of objects as it can 
take in and manage with ease, sees more distinctly all 
the consequences that arise from comparing them one 
with another. When, therefore, it comes afterwards 
to take a review of these its several advances, as b}" this 
means the amount of every step of the investigation is 
fairly laid open to its inspection, by adjusting and put- 
ting these together, in due order and method, it is en- 
abled at last to discern the result of the whole. And 
thus, as before in the composition of our ideas, so like- 
wise here in the search and discovery'of truth, we are 
fain to proceed gradually, and by a series of successive 
stages. For these are so many resting places to the 



ELEM£.\'Ti} or LOGR. 193 

Boiiid, whence to look about it, survey the conclusions 
it has already gained, and see what helps they afford, 
towards the obtaining of others which it must still pass 
through, before it reaches the end of the ijivesligation. 
ilence it often happens, that veiy remote and distant 
truths, which lie far beyond the reach of any single ef- 
fort of the mind, are yet, by this progressive method,' 
successively brought to light, and that too with less fa- 
tigue to the understanding than could at first have w^eli 
been imagined. For although the whole process, ta- 
ken together, is frequently much too large to come With- 
in the view of the mind at once ; and therefore, consi- 
dered in that light, may be said truly to exceed its grasp; 
yet the several steps of the inventigatiDn by themselves 
are often easy and manage ible enough, so that by pro- 
ceeding gradually from one to another, and thoroughly 
mastering the parts as we advance, we carry on our re- 
searches with wondrous dispatch, and are at length con- 
ducted to that very truth, with a view to the discovery 
of which the inquisition itself was set on foot. 

Sec. jx...rAIg€bra and Arithmetic, properly speaJiing 
both Arts of Invention. 

But now perhaps it may not be improper, \{ we en- 
deavour to illustrate these observations by an example, 
and set ourselves to trace the conduct and manner of 
the mind, when employed in the exercise of invention. 
There are two great branches of the mathematics pecu- 
liarly fitted \.o furnish us with models in this way. 
Ariihmetic I mean, and Algebra. Algebra is univer- 
sally known to be the veiy art and principle of inven- 
tion ; and in arithmetic, too, we are frequently put 
upon the finding out of unknown numbers, by means of 
their relations and connexions with others that are 
known : as v^^here it is required to find a number equal 
to this sum of two others, or the product of two others. 
I choose to borrow^ my examples chiefly from this last 
science, both because they will be more wnthin the 
reach of those for whom this treatise is principally de- 
signed'pas'TTkewise, because arithmetic furnishes the 
best models of a happy sagacity and management, in 
R 



194 ELEMENTS OF LOGIC. 

classing and regulating our perceptions. So that here 
more than in any other branch of human knowledgej 
we shall have an opportunity of observing, how much 
an orderly disposition of things tends to the ease and 
success of our inquiries, by leaving us to canvass the 
parts separately, and thereby rise to a gradual concep- 
tion of the whole, without entangling ourselves with 
too many considerations at once,^ in any single step of 
the investigation. For it will indeed be found, that a 
dexterity and address, in the use of this last advantage, 
serves to facilitate and promote our discoveries, almost 
beyond imagination or belief. 

Sec. X The method of classing our Perceptions in 

Arithmetic. 

We have already explained the manner of reducing 
numbers into classes and of distinguishing these class- 
es by their several names. And now we are farther 
to observe, that the present method of notation is so 
contrived, as exactly to fall in with this form of num- 
bering. For as in the names of numbers, we rise from 
units to tens^ from tetis to hundreds, from hundreds to 
thousands, ^rc- so likewise in their notation, the same 
figures, in different places, signify these several combi- 
Bations. Thus 2 in the first place, on the right hand 
denotes two units^ in the second place, it expresses so 
many tens, in the third hundreds, in the fourth thou- 
sands. By this means it happens, that when a number 
is w^rittea down in figures, as every figure in it expresses 
some distinct combination, and all combinations toge- 
ther make up the total sum ; so may the several figures 
be considered as the constituent parts of the "number. 
Thus the number 2436, is evidently, by the very nota- 
tion, distinguished into four parts, marked by the four 
figures that serve to express it. For the first denotes 
t'jvo thousand, the second, J^w?- hundred, the third thirty 
or three tens, and the fourth six. These several parts, 
though they here appear in a conjoined form, may yet 
be also expressed separately thus, 2000, 400, 30, and 
€j and the amount is exactly the same. 



ELEMENTS OP LOGIC. 195 

Sec. XI The helps thence derived towards an easy ad- 
dition of 7iuiribers. 

This then being the case, if it is required to find a 
number equal to the sum of two others given ; our bu- 
siness is, to examine separately these given numbers, 
and if they appear too large and bulky to be dealt with 
by a single effort of thought, then, since the very nota- 
tion distinguishes them into different parts, ^ve mu>t 
content ourselves v/ith considering the parts asunder, 
and finding their sums one after another. For since 
the whole is equal to all its parts, if we find the sums 
of the several parts of which any two numbers consist. 
we certainly find the total sum of the two numbers. 
And therefore, these different sums, united and put to- 
gether, according to the established rules of notation 
will be the very number we are in quest of. Let it be 
proposed for instance, to find a number equal to the 
sum of tiiese two: 243G, and 4552. As the finding-; 
of this by a single effort of thought would be too vio- 
lent an exercise for the mind, I consider the figures, 
representing these numbers, as the parts of which they 
consist, and therefore set myself to discover their suras 
one after another. Thus 2, the first figure on the 
right hand of one, added to 6, the first figure oii 
the right hand of the other, makes 8, which is thereforr^ 
the sum of these two parts. Again, the sum of o 
and 3, the two figures or parts in the second place, is 
likewise 3. But now as figures in the second place; 
denote not simple imifs, but tens ; hence it is plaii:, 
that 5 and 3 here, signify five tens and three tens, ov 
50 and 30, whose sum therefore must be eight ie7is ov 
80. And here again, I call to mind, that having al- 
ready obtained one figure of the sum, if 1 place that 
now found immediately after it, it will thereby stand 
also in the second place, and so really express, as it 
ought to do, eight tens, or 80. And thus it is happi- 
ly contrived, that though in the addition of the tens, 
I consider the figures composing them as denoting on-- 
ly simple imiis, which makes the operation easier and 
less perplexed ; yet by the place their sum obtains in the 
niimber found, it expresses the real amount of the parts 



,196 e;.ement3 of logic. 

added, taken in their full and complete values. TI>e^ 
same thing happens in summing the hundreds and thou- 
sands ; that is, though the figures expressing these 
combinations, are added together as simple units ; yet 
their sums, standing in the third and fourth places of 
the number found, thereby really denote the hundreds 
.'■ind thousands, and so represent the true value of the 
parts added. 

Sec. xu.... Because in the several steps by 'which it i^ 
carried on, the mind is put to little or no ^fatigue. 

Hence then we have a manifest proof of the great 
:idvantages derived from an artful method of classing 
our perceptions. For as the numbers themselves are by 
this means distinguished into different parts which 
brings them more readily within the compass of the un- 
'ierstanding ; so by taking these parts separately, the 
operations about numbers are rendered very easy and 
simple. And indeed it is particularly worthy our no- 
tice, and though in adding two very large numbers to- 
gether, the whole process is of sufficient length ; yet 
the several steps by which it is conducted, are managed 
with incredible dispatch, and scarce any fatigue to the 
mind. This is apparent in the example given above, 
where we see, that in every advance from one part to 
another, nothing more is required than to add together 
the two figures in the like places of the numbers to be 
summed. But what is yet more wonderful, though in 
the progress of a long operation, the figures rise in Iheir 
value as we advance, and grow to signify thousands, 
millions^ hillions, <^'C. yet so happily are they contriv- 
ed for expressing the different parts of numbers,- 
that in every step of the procedure we consider them 
as denoting only simple units^ all other deficiencies be- 
ing made up, by the places their sum.s obtain in the to- 
tal amount. And thus it is so ordered in this admira- 
ble form of notation, that however large the numbers 
are that come under examination, they are neverthe- 
less managed with the same ease as the most simple 
and obvious collections ; because in the several opera- 
tions about them, the mind is neither tied down to 



ELEMENTS OF LOGIC. 197 

the view of too many parts at once, nor entangled with 
any considerations regarding- the bulk and compositibn 
of those parts. 

Sec. xiii^..This Jarther Illustrated by an Example in 
Multiplication. 

And if these advantages are so very manifest in the 
first and simplest rules of arithmetic, much more do they 
discover themselves in those that are intricate and com- 
plex. Let a man endeavour in his thoughts to find 
the product of two numbers, each consisting of twen^ 
ty or thirty places, and that without considering the 
parts separately ; I believe he will soon be sensible, 
that it is a discovery far be^^ond the limits of the hu- 
man mind . But now in the progressive method above ex- 
plained,. nothing is more simple and easy. For if we take 
the first figure on the right hand of the one number, 
and by it multiply «very figure of the other separately ; 
these several products, connected according to the esta- 
blished laws of notation, must truly represent the total 
product of this other, by that part of the multiplying 
number. Let us suppose for instance, the figure in 
the units place of the multiplier to be 2, and the- three 
last places of the multiplicand to be 432. Then, 2 
multiplying 2 produces 4, which therefore is the first 
part of the product. Again, 2 multiplying 3 pro- 
duces 6. But now 3 standing in the second place of 
the multiplicand, denotes its real value three tois^ or 
30, which therefore taken twice, amount to six tens, or 
60. And accordingly the figure 6, coming after 4 al- 
ready found, is thereby thrown into the second place 
of the product, and so truly expresses 60, its full and 
adequate value. The same thing happens in multi- 
plying 4, which standing in^the place of hundreds, its 
product by 2 is 800. But this very sum the figure 8, 
produced from 2 and 4, really denotes in the total pro- 
duct. Because coming after 64, the two parts alrea- 
dy found, it is thereby determined to tlic third place, 
where it of course expresses so many hundreds. . This 
process, as is evident, may be continued to any length 
vm. please ; aud it is remarkable, that in like manner as . 



198 ELEMENTS OP L0Gi«. 

in. addition, though the value of the figures in the muUi* 
plicand continually rises upon us, yet we all along pro- 
ceed with them as simple units ; because the places of 
the several products in the total amount, represent the 
just result of multiplying the figures together, according 
to their true and adequate value. 

Sec. XIV..,. Of the disposition of the several Products in 
order to Addition. 

Having thus obtained the product by the first figure 
of the multiplier, we next take that in the second place, 
and proceed with it in the same manner. This second 
operation gives us the effect of that figure, consider- 
ed as a simple digit. But as it stood in the second 
place, and therefore really denoted so many tens, hence 
it is plain, that the product now gained must be yet 
multiplied by ten, in order to express the true product 
sought. This is accordingly done in the operation, by 
placing the first figure of this second product under 
the second figure of the first product. For this, whea 
they come to be added together, has the same effect 
as annexing a cypher, or multipljnng by ten, as every 
©ne knows who is in the least acquainted with the rules. 
of arithmetic. In like manner, when we multiply by 
tbe figure in the third place, as this new product i& 
placed still one figure backwards, we do in effect an- 
aex two cyphers to it, or multiply it by a hundred. 
And this we ought certainly to do ; because having 
considered the puitiplying figure as denoting only sim- 
ple units, when it really expressed &o many hundreds, 
the first operation give§ no more than the hundredth 
part of the true product. The case is the same in 
multiplying by the fourth or fifth figures, because, the 
products still running badiwards, we thereby in effect 
arnnex as many cyphers to them as bring them up se- 
yerally to their respective adequate value. By this 
means it happens, that though the figures of the mul^ 
tiplier in every adv?ince, denote siili higher and higher 
©om.bi nations, yet we all along proceed with them a& 
aiuipl 6 digits ; the disposition of the several products 
in, ©rder to addition making up for ail the deficiencies 



ELEMEKTS OF LO6IC. Idd 

that arise from this way of considering them. When 
in this method of procedure, tve have obtained the pro- 
duct of the multiplicand into all the different parts ot 
the multiplier, by adding these products together we ob- 
tain also the total product of the two numbers. For 
since the whole is equal to all its parts, nothing is more 
evident, than that the product of any one number into 
another, must be equal to its product into all the parts 
of that other : and therefore the several partial products 
united into one sum, cannot but truljr represent the real 
product sought. 

Sec. XV Arithmetical operations, by being carried on 

in a Progressive method, rendered easy and intelligijle. 

Thus we see, that in questions of multiplication 
though the whole process is sometimes sufficiently long 
and tedious, 5'et the several steps by which it is carried 
on are all very level to the powers of the understand- 
ing. For from the account given above it appears, that 
nothing more is required in any of them than barely 
to multiply one digit by another. But now this easy 
rule of operation is wholly derived from the before-men- 
tioned address in classing our perceptions. For to this 
it is owing, that the numbers under consideration are 
distinguished into parts, and that the several parts are 
also clearly represented to the mind in the very form of 
notation. Now as these parts have an invariable re- 
lation one to another, and advance in their value by an 
uniform law of progression ; the understanding by 
means of such a link can easily hold them together, 
and carry its views from stage to stage without per- 
plexity or confusion. Hence it happens, that how- 
ever large and mighty the numbers are, so far as to ex- 
ceed the immediate grasp of the mind ; 5''et by run- 
cing gradually through the several combinations of 
which they are made up, we at length comprehend 
them in their full extent. And because it would be 
impossible for the understanding to multiply very larg^ 
cumbers one into another, by a simple effort of thought *, 
therefore here also it considers the parts separately, 
^ffid, taking them in an orderly series, advances by a 



2t)0 ELEMENTS OF LOGIC 

variety of successive steps. It is true, indeed, in fiie 
progress of the operation, the several figures rise in their 
value : but this consideration enters not the work it- 
self. For there, as we have already seen, though the 
characters are taken as denoting only simple units, yet 
the order and disposition of the partial products, exhib- 
its each according to its real amount. Hence in every 
step, we have only to multiply one digit by another, 
which as it is attended with scarce any difficulty, the 
whole process is carried on with wondrous dispatch. 
And thus by a series of easy operations, we at length 
rise to discoveries, which in any other method of pro- 
cedure, would have been found altogether beyond the 
reach of the mind. 

Sec. XVI The art of Classing our Perceptions the 

great Mean and Instrument of Invention. 

Since therefore by a due and orderly disposition of 
our ideas, we can bring the most wide and extended 
objects up»n a level with the powers of the understand- 
ing : and since by this also we abridge the fatigue and 
labour of the mind, and enable it to carry on its re- 
searches in a progressive method, without which con- 
trivance, almost all the more remote and distant truths 
of the sciences must have lain forever hid from oup 
knowledge ; I think we may venture to affirm, that the 
art of regulating and classing our perceptions is the 
great mean and instrument of invention. It is for this 
reason that I have endeavoured in so particular a man- 
ner to illustrate it from examples in numbers ; because 
we have here not only a perfect model of the art itself, 
but see also in the clearest manner, what helps it fur- 
nishes towards a ready comprehension of objects, and a 
masterly investigation of truth. Nor let any one find 
fault, as if we had insisted rather too long upon matters 
that are obvious and known to all. For I am. apt to 
think, that though very few are strangers to the re- 
ceived method of notation, and the common rules of 
opeFation in arithmetic ; yet it is not every one that 
sets himself to consider the address and sagacity that 
»ay be sees in the contrivance of them, or to unr^ivel 



ELEMENTS OP LOGIC. SOI 

those principles of investigation, which we have here 
so clearly deduced from them. And this I take to be 
the reason, that we sometimes meet with instances of 
men, who though thoroughly versed in the art of in- 
vention ; vv'ith regard to some particular branches of 
knowledge ; yet if taken out of their usual tract, find 
themselves immediately at a stand, as if wholly bereft 
of genius and penetration. With such men invention 
is a mere habit, carried on in a manner purely mecha- 
nical, without any knowledge of the grounds and rea- 
sons upon which the several rules of investigation are 
iounded. Hence they are unfurnished with those gene- 
ral observations, which may be alike usefully applied 
in all sciences, with only some little necessary varia- 
tions, suited to the nature of the subject we are upon. 
And indeed I know of no surer way to arrive at a 
fruitful and ready invention, than by attending care- 
fully to the procedure of our own minds, in the exer- 
cise of this distinguished faculty ; because from the 
particular rules relating to any one branch, we are 
often enabled to derive such general remarks, as tend 
to lay open the very foundation and principles of the 
art itself. 

Sec. XVII.... T/ie manner of proceeding in the resolu- 
tion of Algebraic questions. 

If now we turn our thoughts from arithmetic to a^- 
gehra^ here also we shall find, that the great invention 
lies, in so regulating and disposing our notices of 
things, that we may be enabled to proceed gradually in 
the search of truth. For it is the principal aim of this 
science, by exhibiting the several relations of things in 
a kind of symbolical language, so to represent them to 
the imagination, as that we may carry our attention 
from one to another, in any order we please. Hence 
however numerous those relations are, yet by taking 
only such a number of them into consideration at once, 
as is suited to the reach and capacity of the under- 
srauding, we avoid perplexity and contusion in our re- 
searches, and never put our faculties too much upon 
the stretch, so as to lose ourselves amidst the multi- 



202- ELEMENTS OF LOGIC. 

plicit}' of our own thoughts. As therefore in arithm.€- 
tic, we rise to a just conception of the greatest num- 
bers as considering them made up of various progres- 
sive combinations ; -so likewise in algebra, those man- 
ifold relations that often intervene, between known 
and unknown quantities, are clearly represented to the 
mind, by throwing them into a series of distinct equa- 
tions. And as the most difficult questions relating to 
numbers are managed with ease ; because we can take 
the parts or figures separately, and proceed with them 
one after another ; so also the most intricate problenrs 
of algebra are in like manner readily unfolded, by ex- 
amining the several equations apart, and unravelling 
them according to certain established rules of opera- 
tion. And here it is well v/orth our notice, that in 
verj^ complicated problems, producing a great number 
of different equations, it for the most part so happens, 
tliat every one of them includes a variety of unknown 
quantities. When therefore we come to solve them 
separately,.!^ it would too much distract and entangle 
the mind, to engage in the' pursuit of so many differ- 
ent objects at once ; our first business is, by artfully 
coupling the several equations together, or by the va- 
rious ways of multiplication, subtraction, addition, and 
substitution, to derive others from them more simple, 
until at length by such a gradual process we arrive at 
some new equation, with only one unknown quantity. 
This done, we set ourselves to consider the equation 
last found, and having now to do with an object suit- 
ed to the strength and capacity of the mind, easily by 
the established rules of the art, discover the quantity 
sought. In this manner we proceed with all the se- 
veral unknown quantities one after another, and having 
bj^ a series of distinct operations traced them separate- 
ly, the question is-thereby completely resolved. 

Sec. xvni...,Of those other Artifices ziohich may he 
considered as Subsidiary helps to Invention, 

Hence it appears, that the business of invention, as 
pract sed in algebra, depends entirely upon the art of 
abridging our thoughts, reducing the number of par^ 



ELEMENTS OF LOGIC. 20o 

tkulars taken under consideration at once to the few- 
est possible, and establishing that progTessive method 
of investigation, which we have already so fully ex-" 
plained from examples in arithmetic. 1 might easily 
show that the same observation holds equally in other 
sciences ; but having already exceeded the bounds I 
at first prescribed to myself in tiiis chapter, shall only 
add, that besides the grand instruments of knowledge 
already mentioned, there are innumerable other artifi- 
ces, arising out of the particular nature of the subject 
we are upon, and which may be considered as subsidi- 
ary helps to invention. T'nis in geometry, many de^ 
monstrations of problems and theorems are wholly de- 
iivad f:om the construction of the figure made use of, 
and the drawing of lines from one point to another. 
In like manner in algebra, the devising of proper equa- 
tions from the conditions of the question proposed, and 
contriving neat expressions for the unknown quanti- 
ties, contribute not a little to the eas}^ solution of pro- 
blems. And when we have even carried on the inves- 
tigation to some single equation with onlj'" one unknown 
ejuaatity ; as that unknown quantity may be variously 
perplexed and entangled with others that are known, 
so as to require a multiplicity of difterent operations, 
beiore it can be disengaged, which often . involves us in 
long and intricate calculations, and brings surds and 
irrational quantities in our way ; algebraists, to pre- 
vent in some measure these inconveniences, and short- 
en as much as possible the process, have fdlen upon 
several methods of substitution, which are of great ser- 
vice in very complicated questions. But these and such 
like artifices of invention, cannot le explained at 
length in this short essay. It is enough to have given 
the reader a hint of them, and put him in the way of 
u iravelling them himself, when he conies to apply his 
thoughts to those particular branches of knowledge 
where they are severally made use of. 

Sec. XIX. ...Of the great ad~cania sees arising from a 
hajjpy Notation or expression of our Jlioughls., 

Tliere U one thing, however, that m a particular 



^04 ELEMENTS OP LOGIC. 

manner deserves to be taken notice of, before we dis- 
miss this subject ; and theit is the great advantages that 
may redound to science, by a happy notation or ex- 
pression of our thoughts. It is owing entirely to thi^, 
and the method of denoting the several combinations 
of numbers by figures standing in different places, 
that the most complicated operations in arithmetic are 
managed with so much ease and dispatch. Nor is it less 
apparent, that the discoveries made by algebra, are 
wholly to be imputed to that symbolical language made 
use of in it. For by this means we are enabled to repre- 
sent the relations of things in the form of equations, and 
by variously proceeding with these equations, to trace 
©ut step by step the several particulars we are in 
quest of. Add to all this, that by such a notation, the 
eyes and imagination are also made subservient to the 
discovery of truth. For the thoughts of the mind rise 
\ip and disappear, according as we set ourselves to call 
them into view ; and therefore without any particular 
method of fixing and ascertaining tiiem as they occur, 
the retrieving them again when out of sight, would of- 
ten be no less painful than the very first exercise of de- 
ducing them one from another. When therefore in 
the pursuit of truth we carry our attention forward from 
one part of the investigation to another, as never- 
theless we have frequent occasion to look back upon 
the discoveries already passed through, could these be 
no otherwise brought into view, than by the same 
course of thinking in which they were first traced, so 
many difierent attentions at once must needs greatly 
distract the mind, and be attended with infinite trou- 
ble and fatigue. But now, the method of fixing and 
ascertaining our thoughts by a happy and well-chosen 
notation, entirely removes all these obstacles. For 
thus, when we have occasion to run to any former dis- 
coveries, as care is taken all along to delineate them 
in proper characters, we need only cast our eye upon 
that part of the process v/here they stand expressed, 
which will lay them at once ©pen to the mind, in their 
true and genuine form,. By this means we can at any 
tl^etake a quick and ready survey of our progress, and 



ELEMENTS OF L60IC. 20i> 

xunning- over the several conclusions already gained, 
see more distinctly what Iielps they furnish towards the 
obtaining of those others we are still in pursuit of. Nay, 
further, as the amount of every step of the investigation 
lies fairly before us, by comparing them variously 
among themselves, and adjusting them one to another, 
we come at length to discern the result of the whole,. 
and are enabled to form our several discoveries into an 
uniform and well-connected system of truths, which is 
the great end and aim of all our inquiries. 

Sec. XX ... . Recapiiula(ion . 
Upon the whole then it appears, that in order to pro- 
ceed successfully in the exercise of invention, we must 
endeavour as much as possible to enlarge the capacity 
of the mind, by accustoming it to wide and comprc- 
liensive views of things : that v,'e must habituate ouj'- 
selves to a strong and unshaken attention, which care- 
fully distinguishes all the circumstances that come in our 
way, and lets nothing material slip its notice : in fine, 
that we must furnish ourselves with an ample variety of 
of intermediate ideas, and be much in the exercise of 
singling them but an i applying them for the discovery 
of truth. These preparatory qualifications obtained, 
what depends upon art lies chiefly in the manner of 
combining our perceptions, and classing them together 
with address, so as to establish a progressive method of 
investigation. And here it is of great importance to 
contrive a proper notation or expression of our thoughis, 
such as may exhibit them according to their real appear- 
ance in the mind, and distinctly represent their several 
divisions, classes, and relations. This is clearl}'- seen 
in the manner of computing by figures in arithmetic, but 
more particularly in that symbolical language, which 
hath been hitherto so successfully applied in the unravel- 
ling of algebraical problems. Thus furnished, we may 
at any time set about the investigation of truth ; and if 
we take care to note down the several steps of the pro- 
cess, as the mind advances from one discovery to anoth- 
er, such an arrangement or disposition of our thoughts 
constitutes what is called the method of invention. For 
S 



206 ELEKi^NTS OF LOGIC. 

thus it is plain that we follow the natural procedure of 
the understanding, and make the truths we have unra- 
velled to succeed one another, according to the order in 
which they present themselves to the mind, while em- 
ployed in tracing and finding them out. And here again 
it well deserves our notice, that as by this means the 
whole investigation lies distinctly before us ; so by 
comparing the several steps of it among themselves, 
and observing the relation they bear onv^ to another, we 
are enabled to form our discoveries into a regular sys- 
tem of knowledge, where the truths advanced are duly 
linked together, and deduced in an orderly series from 
first principles. This other manner of combining our. 
thoughts, is distinguished by the name of the method of 
science, which therefore now offers itself to be explain- 
ed, and is accordingly the subject of the ensuing chap- 
ter. 



CHAP. II. 

OF THE METHOD OF SCIENCE. 



Sec. I. ...Knowledge as derived from the coniemplaiion 
of our Ideas, of a necessary and unchangeable nature ; 

In order to give the juster idea of the rules peculiar 
to this species of method, and establish them upon 
their proper foundation, it will be necessary to ~begin 
with settling the meaning of the word science, and show- 
>ng to what parts of human knowledge that term may 
be most fitly applied. We have already observed, in 
the first chapter of the second book, that there are three ^, 
several ways of coming at the knouledge of truth^^jft 
First, by contemplating the ideas in cur own minds. ^^ 
Secondly, by the information of the senses. Thirdly, 
by the testimony Oi others. When we set ourselves to 
consider the ideas in our own minds, -.ve variously com- 
pare them together, in order to judge of their agree- 
ment or disagreement. Now as all the truths deduced 
in this way, flow from certain connexions and relations, 
•lis'r.erned between the ideas themseJves : and as whew 



ELEMENTS OF LOGIC. 207 

the same ideas are brought into comparison, the same 
relations must ever and invariably subsist between 
them ; hence it is plain, that the knowledge acquired 
by the contemplation of our ideas, is of a necessary and 
unchangeable nature. But farther, as these relations 
between our ideas, are not only supposed to be real ia 
themselves, but also to be seen and discerned by the 
mind ; and as when we clearly perceive a connexion or 
repugnance between any two ideas, we cannot avoid 
judging them to agree or disagree accordingly ; it evi-. 
dently follows that ouc knowledge of this kind is at- 
tended with absolute certainty and conviction, inso-. 
much, that it is impossible for us to withhold our assent, 
'or entertain any doubt as to the reality of truths so offer- 
ed to the understanding. The relation of equality bc« 
tween the whole and all its parts, is appareiit to every 
one who has formed to himself a distinct notion of what 
the words rvhole and part stand for. No man, there- 
fore, who has th.ese two ideas in his mind, can possibly 
doubt of the truth of this proposition, that the 'JvJiole h 
equal to all its parts. For this would only be endea- 
vouring to persuade himself, that that was not, which 
he plainly and unavoidably perceives to be. So that in 
all cases, where we discern a relation between any of 
cur ideas, whether immediately by comparing the one 
with another, or by means of intermediate ideas, that 
lay it open distinctly to the understanding ; the know- 
ledge thence arising is certain and infallible. I say in- 
faliible ; because we not only perceive and- own the 
truth of propositions so offered to the mind, but having 
at the same time a clear view of the ground on which 
our assent rests, are entirely satisfied within ourselves, 
tha+ we cannot possibly be deceived in this percep- 
tion. 

Skc. II Is Jlozi'ing from the inforiiinthn of the seiisa, 

begets undoubted assurance, but excludes not all possi- 
bility of being deceived^ 

This second way of coming at knowledge, is by the 
means of the senses. From them w1» receive inform.a- 
tion of the existcnceof objects without us, of the union 



HOB ELEMENTS OF LOGIC. 

aTid conjanction of different qualities in the same sub- 
.ject, and of the operations of bodies one upon another. 
Thus our eyes teil us, that there is in the universe such 
a body as we call the sun, our sight and touch, that 
light and heat, or at least the power of exciting those 
perceptions in us, co- exist in that body ; and lastly, by 
the same sight we also learn, that fire has the power of 
dissolving metals, or of reducing wood to charcoal and 
ashes. But now with regard to this kind of knowledge 
we are to abserve, that though when the organs of the 
body are rightly disposed and operate in a natural way, 
we never doubt die testimony of our senses, but form 
most of the schemes of life upon their information : yet 
are not the trutlis of this class attended with that abso- 
lute and infallible assurance, which belongs to those de- 
rived from the contemplation of our own ideas. We 
find that the senses frequently represent objects as real- 
ly existing, which yet have no being but in our own 
imaginations ; as in dreams, phrensies, and the deliri- 
ums of a fever. A disorder too in the organs, makes us 
often ascribe qualities to bodies, entirely different from 
those they appear to possess at other times. Thus a 
man in the jaundice shall fancy every object presented 
To him yellow ; and in bodily distempers, where the 
taste is greatly vitiated, what naturally produces the 
idea of sweetness, is sometimes attended with a quite 
contrary sensation. It is true, these irregularities nei- 
ther ought, nor indeed do they, with considerate men, in 
any ways tend to discredit the testimony of experience. 
He that, awake, in his senses, and satisfied that his or- 
gans operated duly, should take it into his head to doubt 
whether fire would burn, or arsenic poison him, and 
therefore rashly venture upon these objects., would soon 
be convinced of his error, in a way not much to his lik- 
ing. As nevertheless the senses do sometimes impose 
upon us there is no absolute and infallible security that 
they may not at others ; therefore the assurance they 
produce, though reasonable, satisfying, and sufficient- 
ly well founded, to determine us in the several actiens 
and occurrences of life, is yet of such a nature, as not 



ELEMENTS OF LOGIC, 



209 



necessarily to exclude" all possibility of being deceived. 
Hence some men go so far as to maintain, that we, ought 
to distrust our senses altogether ; nay, whole sects among 
the ancients, because of this bare possibility, which 
really extends no farlher than to matters of experience 
and testimony^ yet established it as a principle, that we 
ought to doubt of every thing. Nor are there wanting 
philosophers among the moderns, who, upon, the same 
grounds, deny the existence of bodies, and ascribe the 
perceptions excited in us, not to the action of external 
matter, but to certain established laws in nature, which 
Operate upon us in such manner as to produce all those 
several effects that seem to flow from the real presence 
of objects variously affecting our perception. It is not 
niy design here to enter into a particular discussion of 
these matters : all I aim at, is to show, that the testi- 
mony of the senses, though sufficient to convince sober 
and reasonable men, j'et does not so unavoidably extort 
our assent, as to leave no room for suspicion or dis- 
trust. 

Sec. III. ....^5 founded upon testimony, is of a still more 
certain nature, though in many cases embraced iciihout 
wavering or distrust. 

The third and last way of coming at truth is by the 
report and testimony of others. This regards chiefly 
past facts and transactions, which, having no longer 
any existence, cannot be brought w ithin the present 
sphere of our observation. For as these could never 
have fallen under our cognizance, but by the relations 
of such as had sufficient opportunities of being inform- 
ed ; it is hence apparent, that all bur knowledge of this 
kind is wholly founded upon the conveyance of testi- 
mony. But now, although this in many cases is a suffi- 
cient ground of assent, so'as to produce a ready belief 
jn the mind, yet is it liable to still greater objections 
than even the reports of experience. Our senses, it is 
true, on some occasion-s deceive us, and therefore they 
may possibly OiJ). others. But this bare possibility 
creates litt'le or no'distrust; because there are fixed 
rules, of judging, when they operate according to na . 
S 2 



:^10 ELEMENTS OF LOGIC, 

ture, and when thej'' are prevented or given up to csi" 
price. It is otherwise in matters of mere human testi- 
iTiony. For there, besides the supposition that the per- 
sons themselves may have been deceived, there is a 
farther possibility, that they may have conspired to im- 
pose upon others by a false relation. This considera- 
tion has the greater weight, as we frequently meet with 
s-uch instances of disingenuity among men, and know 
it to be their interest in some particular cases, to dis- 
-semble and misrepresent the truth. It would, never^ 
theless, be the height of folly, to reject all human tes- 
timony without distinction because of this bare possi- 
bility. Who can doubt whether there ever were in the 
world such conquerors as Alexander and Julius Caesar? 
There is no absolute contradiction, indeed, in suppos- 
ing, that historians may have conspired to deceive us. 
But such an universal concurrence to a falsehood, with- 
out one contradicting voice, is so extremely improba- 
ble, and so very unlike what usually happens in the 
world, that a wise man could as soon persuade himself 
to believe the grossest absurdity, as to admit of a sup- 
position £0 remote from every appearance of truth. , 
Hence the facts of history, when well attested, are 
readily embraced by the mind ; and though the evidence 
attending them be not such as produces a necessary and 
infallible assurance, it is yet abundantly sufficient to 
justify our belief, and leave those without excuse, who 
vipon the bare ground of possibility, are for rejecting 
entirely the conveyance of testimony, 

^EC. lY...,. Science belongs entirely to that branch of 
knowledge zvldckis derived from the contem'plation of 
fmr Ideas, 

Upon the whole, then, it appears, that absolute ccr- 
;ainty, such as is attended with unavoidable assent, 
and excludes all possibility of being deceived, is to be 
found only in the conten>plation of out own ideas. In 
BQatters of experience and testimony, men, we see, 
may fraiiie pretences for suspicion and distrust : but in 
that part of know4edgeHthich regards the relations of 
©ur idcas^ vioiye such c§n have place. For as all thcs3 



feLEMENTS OF LOGICU 211 

Several relations are either immediately discerned by 
the mind, or traced by means of immediate ideas, 
where self-evidence is supposed to accompanj^ every 
step of the procedure, it is absolutely impossible for a 
man to persuade himself that that is not, which he 
plainly and necessarily perceives to be. Now it is to 
knowledge, attended with this last kind of evidence 
alone, that in strictness and propriety of speech we at- 
tribute the name of science. For science implies per- 
ception and discernment, what we ourselves see and 
cannot avoid seeing ; and therefore has place only in 
matters of absolute certainty, where the truths advanc- 
ed are either intuitive propositions, or deduced from 
them in a way of strict demonstration. And as this 
kind of certainty is no where to be found, but in inves- 
tigating the relations of our ideas; hence it is plain, 
that science, properly speaking, regards wholly the first 
branch of human knov^ledge ; that which we have Said 
is derived from a contemplation of the ideas in our own 
minds. 

Sec. v..,. Our knowledge of the real existence (f Objects 
not Intuitive. 

But here I expect it will be asked, if science andcic- 
rnonstration belong only to the consideration of our 
own ideas, what kind of knowledge it is, that we have 
relating to bodies, their powers, properties, and oper-a- 
tions one upon another ? To this I answer, that we 
have already distinguished it by the name o( natural 
©r experimental. But that we may see more distinctly 
wherein the difference between scientijical and natural 
knowledge lies, it may not be improper to add the fal- 
lowing observations. When we cast our eyes towards 
the sun, we immediately conclude, that there exists ae 
^bject without us, corresponding to the idea in our 
minds. We are, however, to take notice, that this con- 
clusion does not arise from any necessary and unavoid- 
able connexion discerned, between the appearance of 
the idea in the mind, and the real existence of the ob- 
ject without us. We all know by experience, that ide^s 
osay be exciUffll, and that too by a seeming operation 



212 ELEMENTS OF LOGIC. 

of objects upon our senses, when there are in fact no 
suctj objects existing ; as in dreams, and the deliriums 
of H ;ever. Upon what then is the before mentioned 
concJus'on properly grounded ? Why, evidently upon 
this: tbat :^s we are satisfied our organs operate duly, 
and know that every effect must have a cause, nothing 
is more natural than to suppose, that where an idea is 
excited in the mind, some object exists corresponding 
to the idea, which is the cause of that appearance. But 
as this conclusion by what we have seen, is not necessa- 
ry and unavoidable, hence there is no intuition in the 
case, but merely a probable conjecture, or reasonable 
presumption, grounded upon an intuitive truth. 

Sec. VI Absolute Certainty in natural Knowledge con- 

fined to what falls imder our immediate notice. 

Again, when a piece of gold is dissolved in aqua re- 
gia, we see indeed and own the efifect produced, but 
cannot be said, in strictness and propriety of speech, 
to have any perception or discernment of it. The rea- 
son is, because being unacquainted with the intimate 
nature both of aqua regia and gold, w^e cannot, from 
the ideas of them in our minds, deduce why the one 
operates upon the other in that particular manner. 
Hence it is, that our knowledge of the facts and opera- 
tions of nature extends not with certainty beyond the 
present instance, or what falls under our immediate no- 
tice ; so that in all our researches relating to them, 
we must proceed in the way of trial and experiment, 
there being here no general or universal truths, where- 
on to found sa'€?i/;{/?ca/ deductions. Because the solu- 
tion of gold in aqua regia holds in one experiment, 
we cannot thence infallibly conclude that it will hold 
in another. For not knowing upon what it is, in either 
©f these bodies, that the effect here mentioned depends, 
we have no absolute certainty in any new experiment 
we piopose to make, that the objects to be applied one 
to another have that precise texture and constitution 
from which this solution results, Chemists know by 
experience, that b(H]ie;^ which go by the same name^ 
and have the same outward appearance, are not always^ 



ELEMENTS OF LOGIC. 



213 



liovvever, exactly alike in their powers and operations. 
In vain do they often search for those properties in 
one piece of antimony, which on former occasions, 
they may have found in another ; and by this means, 
to their no small mortification, find themselves fre- 
quently disappointed, in very costly and promisin.^ ex- 
periments. Nor have we any express and.positive as- 
surance, that the very bodies with which we have for-'" 
merly made experiments, continue so exactlj' the same, 
as to afford the like appearances in any succeeding 
trial. A thousand changes happen every moment in 
the natural world, without our having the least know- 
ledge oi' perception of them. An alteration in our at- 
mosphere, the approach or recess of the sun, his decli- 
nation towards the north or south, not only vary the 
outward face of things, but occasion many changes in 
the human constitution itself, which we yet perceive 
not vvhen they happen ; nor should ever be sensible of, 
but by the effects and consequences resulting from 
them. And whether alterations analogous to these 
may not sometimes be produced in the frame and tex- 
ture of many bodies that surround us, is what^we can- 
not with certainty determine. Hence, from an ex- 
periment's succeeding in one instance, w^e cannot infal- 
libly argue, that it will succeed in another, even with 
the same body. The thing may indeed be probable, 
and that in the highest degree ; but as there is still a 
possibility that some change may have happened to the 
bod3% unknown to us, there can be no absolute certain- 
ty in the case. 

Sec. vn....What kind of Knon^Jectge of Body would 
deserve the name of Science. 
Had we such an intimate acquaintance with the 
structure both of aqua regia and gold, as to be able 
thence to discern why the one so operates upon the 
other as to occasion its dissolution ; insomuch that 
from the ideas of them in our own minds, we could 
clearly deduce, that bodies of such a make applied one 
to another, must necessarily produce the effect here 
mentioned ; our knowledge would then be scieniificaU 



214 ELEMENTS OP LOGIC. 

and stand upon the foundation either of intuition or 
demonsiraiion, according as the perception was imme- 
diate, or attained by means of intervening ideas. In 
this case, therefore, having two standard ideas in our 
minds, whose relations we perfectly well know ; wher- 
ever we found objects conformable to these ideas, we 
could then pronounce with certainty, that the applica- 
tion of them one to another would be attended with the 
above effect : because, whatever is true in idea, is un- 
avoidably so also in reality of things, where things ex- 
ist answerable to these ideas. If it be true in idea, 
that a parallelogram is the double of a triangle, stand- 
ing upon the same base, and between the same paral- 
lels ; (he same will be true of every real triangle and 
parallelogram, that exist with the conditions here men- 
tioned. We are likewise to observe, that the changes 
to which bodies are daily liable, could produce no con- 
fusion or perplexity in natural knowledge, did it stand 
upon the foundation here mentioned. For in such a 
case, the powers and properties of objects being dedu- 
ced from the ideas of them in our own minds, would 
no otherwise be applied to things* really existing, than 
as these things are found perfectl}'- conformable to our 
ideas. Vv hen, therefore, an alteration happened in any 
body, as it would by this means differ from that stand- 
ard idea whence its former properties were seen to -flow, 
we must of course be sensible, that some suitable change 
would follow in the properties themselves, and that its 
powers and operations, in regard of other bodies, would 
not be in all respects the same. 

Sec. Yiu..., Experience the only foundation of -Natural 

Knowledge. 

But what is still more remarkable, we should, upon 
this supposition, be able to determine the mutual ac- 
tion and influence of bodies, without having recourse 
to trial or experiment. Had we, for instance, a perfect 
knowledge of the inlimate nature and composition of 
an animal body, and of that particular poison that is 
infused into it by the bite of a viper, so as clearly and 
distinctly to discern how they are adapted one to aii^- 



ELEMENTS OF LOGIC. 215 

other ; we might thence scientifically deduce, without 
the help of experiments, that the bite of a viper would 
so unhing'e the human fabric, and produce such fer- 
ments and combustions in it, as must necessarily be fol- 
lowed by a total extinction of all the vital functions, 
and leave that admirable machine a mere lifeless lump. 
But as such perfect and adequate ideas of objects, and 
their mutual habitudes one to another, are plainly be- 
3'ond the' reai;h of our present faculties ; it were vain 
for us to think of improving natural knowledge by ab- 
stract reasoning or scientifical deductions. Experience 
is here the true and proper foundation of our judgments, 
nor can we by any other means arrive at a discovery of 
the several powers and properties of bodies. How long 
might a man contemplate the nature of hemlock, exa- 
mine the structure of its parts in a microscope, and tor- 
ture and analyse it by all the processes of chemistry, 
before he could pronounce with certainty the effect it 
v/ill have upon a human body ? One single experiment 
lays ihat open in an instant, which all the wit and in- 
vention of men would never of themselves have been 
able to trace. The same holds in all the other parts of 
natural philosophy. Our discoveries relating to electri- 
city, the powers and properties of the load-stone, the 
force of gunpowder, &c. were not gained by reason- 
ing, or the consideration of our abstract ideas, but by 
means of experiments made with the bodies themselves. 
Hence it happened, that while the philosophy of Aris' 
totle prevailed in the schools, wi^ch dealt much in 
metaphysical notions, occult qualities, sympathies, an- 
tipathies, and such like words without meaning ; the 
knowledge of nature was at a stand-: because men pre- 
tended to argue abstractedly about the things of which 
they had no perfect and adequate ideas v/hereon to 
ground such a method of reasoning. But now in the 
present age, that we have returned to the way of trial 
and experiment, which is indeed the onl}' true founda^ 
tion of natural philosophy ; great advances have alrea- 
dy been made,, and the prospect of etill greater lies be- 
fore ur^. 



216 ELEMENTS OF LOGIC. 

Sec. IX Difference between Scieniijical and Natural 

Knowledge. 

Arid thus at length we may sufficiently understand 
wherein the proper difference lies, between scientifical 
and natural knowledge. In matters of science we ar- 
gue from the ideas in our own minds, and the connex- 
ions and relations they have one to another. And as 
when these relations are set clearly and plainly before 
us, we cannot avoid perceiving and owning them, hence 
all the truths of this class produce absolute certainty hi 
the mind, and are attended with a necessary and una- 
voidable assent. It is otherwise in the case of natural 
knowledge. Intuition and inward perception have here 
noplace. We discern not the powers and properties 
of those objects that surround us, by any view and com- 
parison of the ideas of them one with another, but mere- 
ly by experience, and the impressions they make on 
the senses. But now the reports of sense' happening 
in some instances to deceive us, we have no infallible 
assurance that they may not in others ; which weakens 
not a little the evidence attending this kind of know- 
ledge, and leaves room for suspicion and distrust. Nay, 
what is yet more considerable, as we have no perfect 
and adequate ideas of bodies, representing their inward 
constitution, or laying open the foundation upon which 
their qualities depend, we can forai no universal prepo- 
sitions about them, applicable with certainty in all par- 
ticular instances. Fire, we say, dissolves metals. This, 
though expressed indefinitely, is, however, only a par- 
ticular truth, nor can be extended with absolute assur- 
ance, beyond the several trials made. The reason is, 
that being ignorant of the inward frame and composi- 
tion both of lire and metals ; when objects are offered 
to us under that name, we have therefore no positive 
certainty that they are of the very make and texture, 
requisite to the success of the experiment. The thing 
may indeed be probable in the highest degree ; but for 
want of standard and settled ideas, we can never arrive 
at a clear and absolute perception in the case. 



ELEMENTS OF LOGIC. 217 

Sec. x....The manner of Reasoning in Natural Know- 
ledge. 
As nevertheless, it is certain that many general con- 
clusions in natural philosophy are embraced without 
doubt or hesitation ; na}'", that we form most of the 
schemes and pursuits of life upon that foundation ; it 
will naturally be asked here, Mow come we by this as- 
surance ? 1 answer, not pcientificaliy, and in the way of 
strict demonstration, but by analogy, and an induction 
of experim.ents. We disting:uish fire, for instance, by 
such of its qualities as lie more immediately open to the 
notice of the senses ; among which light and heat are 
the most considerable. Examining still farther into its 
nature, we find it likewise possessed of the power of dis- 
solving metals. But this new property not having any 
necessary connexion that we can trace, with those other 
qualities by which fire is distinguished, we cannot there- 
fore argue with certainty, that wherever light and heat, 
&c. are, the power of dissolving metals co-exists with 
them. 'Tis not till after we have tried the thing in a 
variety of experiments, and found it always to hold, 
that we begin to presume there may be really some 
such connexion, tho' our views are too short and imper- 
fect to discover it. Hence we are led to frame a gene- 
ral conclusion, arguing from what has already happen- 
ed, to what will happen again in the like cases, insomuch 
that where we meet with all the other properties of fire 
in any body, we have not the least doubt, but that upon 
trial, the power above-mentioned will be found to be- 
long to it also. This is called reasoning by analogy ; 
and it is, as we see, founded entirely upon induction, 
and experiments made with particular objects ; the 
more precise and accurate our ideas of these objects are, 
and the greater the variety of experiments upon which 
W'e build our reasoning, the more certain and undoubt- 
ed will the conclusions be. 'Tis in this manner we ar- 
rive at all the general truths of natural knowledge : a? 
that the bite of a certain an imal is mortal ; that a needle 
touched by a loadstone points to the north ; that gravi- 
ty belongs universally to ali bodies ; and innumerable 
others^ which^ though not capable of strict demionstra- 
T 



218 ELEMENTS OP LOGI«. 

tion are nevertheless as readily embraced upon the foun- 
dation of analogy, as the most obvious and intuitive 
judgments ; nay, and become fixed and steady princi- 
ples of action, in all the aims and pursuits of life. 

Sec. XI..., How even Scientifical Reasoning may he in- 
troduced into it. 

And here again it is particularly remarkable, that 
having ascertained the general properties of things by 
analogy, if we proceed next to establish these Sispostu- 
lata in philosophy, we can, upon this foundation, build 
strict and mathematical demonstrations, and thereby 
introduce scientifical reasoning into natural knowledge. 
In this manner, sir /setae Newton having determined the 
laws of gravity by a variety of experiments, and laying 
it down as a principle, that it operates according to 
those laws through the whole system of nature ; has 
thence, in a way of strict demonstration dedaced the 
whole theory of the heavenly motions. For granting 
once X\\\^ postulatum, that gravity belongs universally to 
all bodies, and that it acts according to their solid con- 
tent, decreasing with the distance in a given ratio ; 
what sir Isaac has determined in regard to the planeta- 
ry motions^ follows from the bare consideration of our 
-own ideas.; that is, necessarily 2in6. scientifically. Thus 
likewise \n optics^ if we lay it down as a principle, that 
light is propagated on all side« in right lines, and that 
the rays of it are reflected and refracted according to 
certain fixed and invariable laws, all which is known to be 
true by experience ; we can upon this foundation esta- 
blish mathematically the theory of vision. The same 
happens in mechanics, hydrostatics, pneumatics, &c. 
where from postulata ascertained by experience, the 
whole theory relating to these branches of knowledge 
follows in a way of strict demonstration. And this I 
take to be the reason why many parts of natural philo- 
sophy are honored with the name of sciences. Not that 
they are ultimately founded upon intuition ; but that the 
several principles peculiar to them being assumed upon 
the foundation of experience, the theory deduced from 
these principles is established by scientifical reasoning* 



ELEMENTS OF LOGIC. 21-9 

Skc. xu... Yet still Experience is the ultimate Ground 
of our Assent, 
Could we indeed discern any necessary connexion 
between gravity and the known essential qualities of 
matter, insomuch that it was inseparable from the very 
idea of it ; the whole theory of the planetary motions 
would then be strictly and ^ropeAy scientific al. For 
seeing, from the notion of gravity, we can demonstra- 
tively determine the laws that bodi.es will observe in 
their revolutions, in any known circumstances ; if the 
circumstances relating to any system of bodies can be 
traced, and gravity is supposed essential to them, we 
can then, from the bare consideration of our own ideas, 
deduce all their motions and phenomena. Now this ie 
precisely what sir Isaac has done in regard to our plane- 
tary system. He has determined the circumstances of 
the bodies that compose it, in respect of situation, dis- 
tance, magnitude, &c. all which being supposed, if they 
are essentially actuated by gravity, their several revolu- 
tions and appearances must be equally essential. But 
as the principle of gravitation cannot be accounted for 
by tln^ known qualities of matter, neither can this theo- 
ry be immediately deduced from the idea of body ; and 
therefore, tho' our reasoning in this part of philosophy 
be truly scientifical, yet as the principle upon which 
that reasoning is grounded, is derived from experience, 
the theory itself must needs ultimately rest upon the 
same foundation. And thus even the doctrine of the 
planetaiy motions, though seemingly established by ma^ 
thematical reasoning, falls yet, in strictness and pro- 
priety of speech, under tlie head of natural knowledge. 
For in this precisely consists the difference between 
science, and what we call the philosophy of nai'ure; that 
the one^grounded ultimately on intuition, the other on 
experieWce. As the observation here made holds alike 
m all the other branches of natural philosophy, into 
which scientijical reasoning has been introduced ; it is 
hence apparent, that they are not sciences, in the strict 
and proper sense of the word, but only by a certain 
latitude of expression common enough in all languages. 
What we have therefore said above, relating to the im- 



202 ELEKENTS ©F L06IGV 

possibility of improving natural knowledge,, by scie»- 
tifical deductions, is not contradicted by ahy thing ad- 
vanced in this section. We there meant deductions 
grounded ultimately on intuition, and derived from a 
consideration of the abstract ideas of objects in our own 
minds ; not such as flow 1mm postulata, assmned upon 
the foundation of experience. For these last, as we 
have already observed, are not truly and properly sci- 
cntifical, but have obtained that name merely on ac- 
count of the way of reasoning in which they are collect- 
ed from the said j^ostulata. 

Sec. XIII The manner of Reasoning in Historical 

Knowledge. 

If then absolute and infallible certainty is not to be 
obtained in natural knowledge, much less can we ex^ 
pect it in historical. For here testimony is the only 
ground of assent ; and therefore the possibility of our 
being deceived, is still greater than in the case of ex- 
perience. Not only he who reports the fact may him- 
self have formed a wrong judgment ; but could we eves 
get over this scruple, there is still room to suspect, that 
he taay aim at imposing upon us by a false narration. 
In this case, therefore, it is plain, there can be no in- 
tuition or inward perception of truth, no strict and ab- 
solute demonstration, and consequently no science. 
There is, however, a way of reasoning even here, that 
begets an entire acquiescence, and leads us to embrace 
without wavering, the facts and reports of history. If, 
for instance, it appears, that the historian was a man 
of veracity ; if he was a competent judge of what he 
relates ; if he had sufficient opportunities of being in- 
formed ; if the book that bears his name was really 
written by him ; if it had been handed down to us un- 
corrupted ; in fine, if what he relates is probable in it- 
self, falls in naturally with the other events of that age, 
and is attested by contemporary writers : by these and 
such like arguments, founded partly on criticism, part- 
ly on probable conjecture, we judge of past transac- 
actJons ; and though they are not capable of scientijical 
proof, yet in many cases we arrive at an undoubted as* 



ELEMENTS OF LOGIC. 221 

surance of them. For as it is absurd to demand ma- 
thematical demonstration in matters of fact, because 
they admit not of that kind of evidence ; it is no less 
so to doubt of their reality, when they are proved by 
the best arguments their nature and quality will bear. 

Sec. XIV,... Scepticisms necessarily excluded Jrom mat- 
ters of Science ; 

And thus we see, in the several divisions of human 
knowledge, both what is the ground of judging, and 
the manner of reasoning, peculiar to each. In scienti/i- 
cal knowledge, which regards wholly the abstract ideas 
of the mind, and those relations and connexions they 
have one with another ; our judgments are grounded 
on intuition^ and the manner of reasoning is by demon- 
stration. In natural knowledge, respecting objects that 
exist without us, their powers, properties, and mutual 
operations ; we judge on the foundation of experience 
and reason by induction and analogy. Lastl}'', in histo- 
rical knowledge, which is chiefly conversant about past 
facts and transactions, testimony is the ground of judg- 
ment, and the way of reasoning is by criticism and jsro- 
hahle conjecture. And now I think we are able effect- 
ually to overthrow that absurd kind of scepticism main- 
tained by some of the ancients which brings all propo- 
sitions upon a level, and represents them as equally un- 
certain. What gave the first rise to this doctrine was, 
caprice of certain philosophers, who observing that the 
reports of sense and testimony were in some instances 
deceitful, took thence occasion to suppose that they 
might be so likewise in others, and thereupon establish- 
ed it as a principle, that we ought to doubt of every 
thing. But even with respect to this doubting, we are 
to observe, that it can in fact extend no farther, than to 
matters of experience and testimony, being totally and 
necessarily excluded from scientifical knowled: e. When 
ideas make their appearance in the understanding, it is 
impossible for us to doubt of their being there. And 
when the relations of any of our ideas are cl( arly and 
distinctly discerned by the mind, either imn.e liately. 
T 2 



2f2.2 ELEKEXTS OF LOGIC, 

which is intuition^ or by means of intervening' uiea.^, 
which is demonstration ; it would be in vain for us to 
^'-ndeavour to persuade ourselves that that is not, which 
we plainly and unavoidably perceive to be. In this 
rase, therefore, we cannot withhold our assent ; truth 
forces its wTxy over all opposition, and breaks in with so 
much light upon the mind, as to beget absolute and in- 
/villible certainty. 

Sec. xv....j?«(f to he admitted with caution in matters oj^ 
exiJerience and testimony. 

Indeed in natural and historical knowledge scepticism: 
mayhave place ; because, as we have said, there is a pos- 
sibility of our being deceived.. But then it is t«) be obsery- 
ed that a bare possibility is a very weak ground whereon 
to bottom any philosophical tenet. It is possible, that 
Great Britain may be swallowed up by the sea before 
to-morrow ; but I believe no man is on this account in- 
clined to think that it will be so. It is possible, the 
whole human race may be extinguished the next in- 
stant ; yet this possibility creates no apprehension that 
the thing itself will rcallyhappen. In a word, we ought to 
judge of things by the proofs brought to support themj 
not by bare abstract possibilities ; and when we haye 
all the evidence they are capable of, that alone is suf- 
ficient to convince, though perhaps the contrary cannot 
be shown to imply a contradiction. Will any wise ancj 
considerate man doubt whether there be such a plac6 
ns Africa, because we cannot prove, by any necessary 
•argument, that it is absolutely impossible all tlie rela- 
tions concerning it should be false ? Strict and rigorous 
demonstrations belong not to histor}^ or the philoso- 
phy of Nature. The way of reasoning, in these branchy 
cs of knowledge, is by arguments drawn from expe- 
rience and testimony. And wb.en the truth of any pro- 
position is in this manner sufFicienlly ascertained, inso- 
much that it appears with all the evidence it is capable 
cf, and v/e have as great reason to believe that it i«, as 
we could possibly have, supposing it were, is not this 
upon the matter as satisfactory as a demonstration ? It 
must b€ owned, iiideed, tliere is no inward perception 



ELEMENTS OF LOGIC, 223 

ill the case ; and therefore our assent cannot be said 
to be necessary and unavoidable. Men may in these 
matters be sceptics, if they please ; and if they are re- 
solved upon it, it is in vain to contend with obstinacy 
and perverseness. I cannot, however, but observe, that 
if they will really act up to their own principles, and 
treat all things in good earnest as uncertain, that ad- 
mit not of strict scientifical proof, their conduct must 
be the very madness of folly. No man can demonstrate 
mathematically, that poison has not been conveyed 
into his meat or drink. And if he will be so very cau- 
tious as- not to taste of either, till he has reached this 
degree of certainty, I know no other remedy for him, 
but that in great gravity and wisdom he must die for 
fear of death. The truth of it is, the most zealous 
patrons of scepticism, after all their pretended doubts- 
and scruples find it yet convenient to behave, in the se- 
veral occurences of life, as if the}" gave entire credit to 
the reports of sense and testimony. They will no more 
venture upon a dose ofarsenic, or rush into the midst of 
a glowing furnace,, than if they verily believed death 
would be the consequence. And though in this it must 
be owned they act discreetly, yet have we hence at the 
same time a very convincing argument of the absurdity 
of those notions they affect to entertain. In reality, 
can any thing be more ridiculous, than to give into a 
scheme of thinking, which we find ourselves necessita* 
ted to contradict in almost every occurrence of life ? 
Opinions are not to be taken up out of caprice and fancy, 
but to serve as principles of action, and standing rules- 
of behaviour. When they answer not this main pur- 
pose, thej' arc unavailing and fruitless, and an obstinate 
adherence to them, in spite of repeated admoni- 
tions of experience, justly deserves to be branded for 
folly. We shall not, therefore, attempt to multiply ar- 
^uinents in a matter so obvious, it sufficiently answer- 
ing our present purpose to have shown, that doubting 
and uncertainty have no place in scientifical knowledge, 
and that even in matters of history, and the facts of na- 
ture, an undi.stinguishing scepticism would be in tiwe 
tii.^hest degree absurd. 



224 ELEMENTS ©F LOGIC 

Sec. xvj,,., Science applicable to the Concerns of Human 
Life. 
But here, perhaps, it will be asked, Why all this 
srsighty noise aboul science, when, even according to 
the present account, it seems to be so very capricious 
and arbitrary a thing ? For seeing it is w^holly confined 
to the consideration of our ideas, and we are at liberty 
to frame and combine those ideas at pleasure, this in- 
deed opens a way to castles in the air, of our own 
building, to many chimerical and fanciful systems, 
which men of warm and lively imaginations love to 
entertain themselves with, but promises little of that 
knowledge which is worth a wise man's regard, and 
respects the great ends and purposes of life. Where is 
the advantage of barely contemplating our ideas, and 
tracing their several habitudes and relations, when it 
is in truth the reality of things that we are chiefly con- 
cerned to know, and those respects they bear to us and 
one another? To this I answer: that if indeed our 
ideas no way regarded things themselves, the know- 
ledge acquired by their means would be of very little 
consequence to human life. But since as we have al- 
ready observed, whatever is tru€ in idea, is unavoidably 
so also in the reality of things, where things exists an- 
swerable to these ideas ; it is apparent, that by copy- 
ing our ideas with care from the real objects of nature, 
and framing them in a conformity to those conjunctures 
and circumstances in which we are most likely to be 
concerned, a way is laid open to discoveries of the 
greatest importance to mankind. For in this case, our 
several reasonings and conclusions, holding no less of 
the objects themselves, than of the ideas by which 
they are represented, may be therefore applied with 
certainty to these objects, as often as they fall under 
our notice. Thus mathematicians, have formed to 
themselves ideas of cones, cylinders, spheres, prisms, 
kc. variously compare them together, examine their 
several properties, and lay down rules by which to 
calculate their relative bulk and dimensions. But now 
as bodies answering in figure to these ideas come fre- 
quently under our observation^ we have by this means 



ELEMENTS OP LOGIC. 235 

ao opportunity of applying mathematical knowledge to 
the common concerns of life ; and by determining 
precisely the quantity of extension in each body, can 
the better judge how far they will answer the purposes 
we have in view. The same thing happens in politics 
andmoraIit3\ If we form to ourselves ideas of such 
communities, connexions, actions and conjunctures, as do 
or may subsist among mankind ; all our reasonings and 
conclusions will then respect real life, and serve as 
steady maxims of behaviour in the several circumstances 
to which it is liable. It is not, therefore, enough that 
we set about the consideration of any ideas at random ; 
we must further take care that those ideas truly regard 
things them'^elves ; for although knowledge is always 
certain, when derived from the contemplation of our 
own ideas, yet it is then only useful and worthy our re- 
gard, when it respects ideas taken from tne real objects 
of nature, and strictly related to the concerns of human 
life. 

Sec. XV u.... The method of sc{e7ice begins "oi^ith ascer- 
taining our Ideas ; 

Having thus shown that there is such a thing as 
science, fixed and ascertained the bounds of it, and ex- 
plained its great use and importance in the afifairs of 
mankind ; it now remains that we lay down the 
rules of method peculiar to this branch of know- 
ledge, and give some account of the manner in which 
that certainty and conviction which are inseparable 
from it, may be most naturally and effectually pro- 
duced. Science, as we have said, regards wholly the 
abstract ideas of the mind, and the relations they have 
one to another. The great secret, therefore, of at- 
taining it lies in so managing and conducting our 
thoughts, as that these several relations may be laid 
open to the view of the understanding, and become 
the necessary and unavoidable objects of our percep- 
tion. In order to this we must make it our first care, 
distinctly to frame and settle the ideas about which 
our inquires are to be emplo^^ed. For as the relations , 
subsisting between Ihem can no otherwise be discerned, 



22G- ELEMENTS OP LOGIC. 

than bj comparing' them one with another — and as- 
this comparison necessarily supposes that the ideas 
themselves are actually in the mind, and at that very 
time under our immediate inspection — it plainly fol- 
lows, that all science must begin with fixing and ascer- 
taining those ideas. Now our ideas, as has been al- 
ready observed in the first book, come all very natu- 
rally within the division of simple and complex. Sim- 
ple ideas are excited by actual impressions made upon 
the understanding ; and as they exist under one uni- 
form appearance, without variety or composition, arc 
in no danger of being mistaken, or confounded one 
with another. It is otherwise in our complex concep- 
tions. For these consisting of many simple idea* 
joined together, great care must be taken, that \ve ac- 
quaint ourselves with the true number combined, and 
the order and manner of their connexion. By this 
m^ans alone are these our most intricate notices, kept 
distinct and invariable, insomuch that in all our several 
views of them, they ever have the same appearance, 
and exhibit the same habitudes and respects. Here, 
therefore, properly speaking, the art of knowledge 
begins. For although we find it easy enough to bound 
and settle our ideas, where they consist of but few 
simple perceptions ; yet when they grow to be very 
complicated, it often requires great address and ma- 
nagement to throw them into such views as may pre- 
vent that confusion which is apt to arise from the joint 
consideration of a multiplicity of different objects. 
Hence that gradation in the composition of our ideas 
which we have explained at large in the last chapter 
of the first book. For as they are by this means formed 
into different orders, and these orders arise continually 
one out of another ; the understanding, by taking 
them in a just succession, gradually mounts to the 
highest conceptions, and can, at any time, with incre- 
dible ease and expedition, bring all their parts distinct- 
ly into view. To know, therefore, the full value of this 
contrivance, we must attentively consider the strict 
connexion that obtains between the several classes of 
®ur perceptions wbea disposed in such a scrips. Eve- 



ELEMENTS OF LOGIC. 227 

ry succeeding order is formed out of those combina- 
tions that constitute the rank next below it. And 
as in advancing from one degree to another, we are 
always to proportion the number of notices united, to 
the strength and capacity of the mind ; it is apparent, 
that by such a procedure, the ideas will be thoroughly 
ascertained in every step, and, however large and ;|^ 

bulky, lie yet fairly within our grasp. This obvious- 
ly accounts for that wonderful clearness of apprehen- 
sion, which we often experience within ourselves, even 
in regard to the most complicated conceptions. For 
though the multitude of parts in many cases be great, 
I may say beyond belief, \^et as they have been all 
previously formed into separate classes, and the class- 
es themselves distinctly settled in the understanding ; 
we find it easy, by such a series of steps, to rise to any 
idea, how complex soever, and, with a single glance ^ 

of thought, to embrace it in its full extent. 
Sec. XXIII.... ./5?^c? Communicating them, by means of }^. 

Definitions, ^ 

But it is not enough that we barely form ideas in 
«ur own minds: wejnust also contrive a way to ren- 
der them stable and permanent, that, when they disap- J'^ 
pear upon calling off our attention, we may know how 
to retrieve them again with certainty. This is best 
done by words and descriptions, which serve not only ^^^ 
to subject them to their own review, but also to lay thera if/mi^ 
open to the perception of others. And indeed as one ' ■ ^ 
of the main ends of reducing knowledge into the . ^ 
form of a science is, the easy and advantageous com- 
munication of truth ; it ought always to be our first 
care, when we set about unfolding our discoveries, to 
exhibil the several conceptions to which they relate, 
in a just and accurate series of definitions. For till we 
have distinctly transferred our ideas into the under- 
standings of those to whom we address ourselves, and 
taught their connexion with the appropriated sounds, 
all our reasonings will evidently be without effect. 
If men comprehend not the true import of our 
wordSj aad are therefore Jed by them to bring wroog: 



22S ELEMENTS 0P L©GI«. 

ideas into comparison, they can never sure see eoaaei- 
ions and habitudes that really subsist not. But if, oti 
the contrarjs the terms we use, excite those very per- 
ceptions in others, which they denote in our own 
minds ; then as the several relations pointed out will 
lie fairly open to view, they must needs be discerned 
with great readiness and ease, and stamp the character 
of certainty upon all our deductions. 

Sec. XIX.... TAe names of simple Ideas constitute the 
original and elementary terms of Language, 
Thus we see, that the method of science begins with 
unfolding our ideas, and , communicating them by 
means of definitions. And here it is of great impor- 
tance to observe, that there must be in all languages, 
certain original and elementary names, whence our 
descriptions take tLeir first rise, and beyond which we 
cannot trace the meaning and signification of sounds. 
For since our very definitions are made up of words, 
if we suppose not such primitive and fundamental 
terms, into which they all resolve themselves, and' 
where they at last necessarily terminate, it is evi- 
dent there would be no end of explaining. Now it is 
peculiar to our simple ideas, that they cannot be origi- 
nally excited by words, but must always make their 
first entrance into the understanding by the actual 
operation of objects upon it. When, therefore, in a 
series of definitions, we arrive at the names of these 
ideas, 'tis plain we can push our descriptions no far- 
ther, but are necessitated to suppose, that the percep- 
tions themselves have already found admission into the 
mind. If they have not, definitions avail nothing ; nor 
can they any other way be impressed upon us, than 
by betaking ourselves to the several objects in which 
the power of producing them resides. Hence it ap- 
pears, that the primary article of speech, into which 
the whole of language may be ultimately resolved, 
are no other than the names of simple ideas. These, 
we see, admit not definitions. It is by experience and 
observation, that we grow acquainted with their mean- 
ly, and furnish ourselves with the perceptions they 



ELEMENTS OF LOGIC, 



220 



scn'c to denote. For finding tliat those in whose socie-, 
ty we live, make use of certain articulate sounds, to 
make the various impressions of objects, we too annex 
these sounds to the same impressions, and thus come to 
understand the import of their words. This way of 
knowledge takes place, in regard to all our simple 
ideas ; but in many of those that are complex, as tney 
are the mere creatures of the understanding, -and exist 
no where out of the mind, there are, of course, no real 
objects without us, whence they may be originally ob- 
tained. If, therefore, they could not be communicated 
by descriptions, we should be left wholly without the 
means of transferring them into the minds of others. 
But happily it so falls out, that all complex conceptions 
whatsoever may be distinctly exhibited in definitions. 
For as they are no more than different combinations of 
simple ideas, if these simple ideas have already got 
admission into the understanding, and the names serv- 
ing to express them are known ; it will be easy by de- 
scribing the order, number, and peculiar connexion of 
the notices combined, to raise in the miod of another 
the complex notion resulting from them. 

Sec. XX.... ^ Knowledge of these previously supposed in 
handling any subject scientifically. 

Since then it is by simple ideas and their names, that 
we unfold all the other conceptions of the mind ; it 
manifestly follows, that in handling any subject, scien- 
iijically^ we must always suppose those to whom we ad- 
dress ourselves, previously furnished by experience 
with these first principles and elements of knowledge. 
Nor is this by any means an unreasonable postulatum : 
because the simple ideas that relate to the sciences, be- 
ing few in number, and coming very often in our way, 
it is hardly possible we should be unacquainted with 
them, or not have frequently heard their names in con- 
verse with others. What principally demands our care 
js, to apply those names aright and according to the 
strict use and propriety of the language in which we 
write. 'Tis seldom allowable to change the significa- 
tion of words, especially those by which we denote 



230 ELEMENTS OF LOGIC* 

simple ideas. If, however, such a liberty should at 
any time be found necessary, we may still make our- 
selves understood, by mentioning the idea under its 
common name, and signifying its connexion with the 
newly appropriated sound. Indeed it sometimes hap- 
pens, that new and unusual ideas of this kind are to be 
taken under consideration, which we must therefore 
express by terms of our own invention. In this case, 
as the ideas themselves cannot be laid open by defini- 
tions, we refer to the several objects whence they may 
be obtained ; which though it excites not the percep- 
tions immediately, yet sufficiently answers our purpose, 
by putting men in a way of being furnished witli them 
at pleasure. 

Sec. xxj....The order and connexion of our Definitions, 

This foundation being laid, the communication of 
our complex conceptions by definitions becomes both 
easy and certain. For since the ideas themselves are 
formed into different orders, and these orders arise con- 
tinually one out of another ; nothing more is required 
on our part, than to observe a like method and grada- 
tion in our descriptions. As, therefore, the first order 
of our compound notions is formed immediately from 
simple ideas ; so the terms appropriated to this order 
must be defined by the names of these ideas. And as 
the second and all the succeeding orders arise continu- 
ally out of those combinations that constitute the class- 
es next below them, so the definitions corresponding 
to these different orders gradually take in the terms by 
which the several inferior divisions are regularly and 
successively expressed. In such a series of descriptions, 
it is evident, at first sight, that nothing can be obscure 
and unintelligible. For as it begins with the names of 
simple ideas, whose meaning is supposed to be known 
. — and as in every order of definitions, such terms only 
occur, as have been previously explained in the pre- 
ceding distributions — by advancing regularly from one 
to another, we gradually furnish ourselves with whatev- 
er is necessary towards a distinct conception of all that 
i^ laid before us. Nor is it a small advantage attending 



ELEMENTS OF LOGIC. 231 

this disposition, that the several ideas described are 
hereby excited in the understanding, in the very order 
and manner in which they are framed by a mind ad- 
vancing uniformly from simple to the most complicated 
notions. Hence we see distinctly the various depend- 
ence of things, and being put into that very train of 
thinking which leads directly to science and certainty, 
eiro drawn insensibly to interest ourselves in the pur- 
suit ; insomuch, that while in fact we do no more than 
follow a guide and conductor, we can yet hardly forbear 
fancying ourselves engaged in the actual exercise of de- 
ducing one part of knowledge from another. 

Sec. xxu...,Ofthe immediate and intuitive Relations bc- 
tzveen our Ideas. 

When we have thus fixed and ascertained our ideas, 
and distinctly exhibited them in definitions, we then en- 
ter upon the important task of tracing their several ha- 
bitudes and relations. In order to this, we set about 
comparing them among themselves, and vievv'ing them 
in all the variety of lights, by which we can hope to ar- 
rive at a discovery of their mutual agreem.ent or disa- 
greement. And here it happens, that some relations 
ibrwardly offer themselves to the notice of the under* 
standing, and become the necessary objects of percep- 
tion, upon the very first application of our ideas one to 
another. Those are, therefore, immediately owned, 
and constitute our primary and inJJwiVire judgments, be- 
ing attended with the highest degree of evidence, and 
producing absolute certainty in the mitid. But in many 
cases, the connexion or repugnance between our ideas, 
even when true and real, comes not ^t within our im- 
mediate view, but requires search and examination to 
discover it. On this occasion, we have recourse to in- 
termediate notices, and if by means of thein we cau 
muster up a train of evident and known truths, which, 
disposed in a regular series of argumentation, lead at 
last to a conclusion expressing the relations we are in 
quest of, the proof thence arising is called demonstra- 
tion. 'Now as the conviction attending demonstration, 
is no less necessar}^ and unavoidable than that which 



■J 



%32 ELEMENTS Oy LOGIC. 

proceeds from intuition ; it evidently follows, that whe- 
ther the relations between our ideas are immediately 
discerned by the mind, or whether they are traced by 
means of intervening^ perceptions, in either ca-se we ar- 
rive at science and certainty. This, however, is par- 
ticularly to be observed, that the more remote and dis- 
tant respects, being deduced from such as are obvious 
and self-evident, the propositions expressing these last 
depisind our first notice, and ought to be previously es- 
tablished, before we enter upon higher investigations* 
When, therefore, in the method of science, we have fin- 
ished the business of definitions ; it must be our next 
care, distinctly to unfold in propositions, those immedi- 
ate and intuitive relations, which are necessarily seen 
and owned by the mind, upon the very first comparing 
of our ideas one with another. These propositions have 
obtaincvd the name oi first j)rinciples, because occurring 
first in the order of knowledge, and being manifest of 
themselves, they suppose not any prior truths in the 
mind, whence they may be evidenced and explained. 
It is not needful to enlarge here upon the necessity of 
circumspection and care, in settling, these primitive aijd 
fundamental perceptions. For since the whole super- 
structure of our knowledge rests ultimately upon them, 
it is evident at 6rst sight, that a mistake in this case 
must at once overturn and annihilate all our future rea- 
sonings. But having already explained the nature of 
these propositions in the second book, unfolded tlie no- 
tion of self-evidence, and taught the manner of distin- 
guishing between the truths of this class, and those that 
are demonstrable ; we shall, for the present, wave aqj 
farther consideraj^n of this subject, referring t4e rea- 
der to what is there advanced,, if he desires fuller in- 
formation. 

Sec. XKUi.,..Of the application ofi Self-evident truths in 
demonstrating' such as are remote and distant. 

The first and more immediate relations of our ideas 
being thus pointed out, our next business is, to investi- 
gate such as are remote and distahf. And here it is 
that we have occasion for intermediate notices, and a 



ELEMENTS' GF LOGIC. 233 

skilful application of intuitive truths. But though self- 
evident propositions be the ultimate foundation of our 
reasoning, we are not, on that account, to imagine, 
that the art of improving knowledge lies in assembling, 
at random, a large and comprehensive stock-^f these. 
Even general principles, considered by themselves, 
avail but little towards the investigation of truth. They 
are, indeed, useful as media of certainty, by preserving 
the evidence of our reasoning distinct, which never fail 
to convince, if, being pursued to their source, they are 
found to resolve themselves into, and ultimately termi- 
nate in these principles.. But when we set about the 
increase and enlargement of science, far other helps 
are required. For here the whole secret consists, in 
devising and singling out such intermediate ideas, as, 
being compared with those others whose relations we 
inquire after, may furnish out a train of obvious and 
know^n truths, serving distinctly to investigate the said 
relations. Euclid, in the first book of the elements^ 
has demonstrated, that the three inward angles of a tri- 
angle taken together, are equal to trmo right angles. The 
reasoning, by which he establishes that proposition, re- 
solves itself into this general principle: things equal 
to one and the same things are equal to one another. 
Will any one, however, pretend to say, that a bare 
consideration of the principle itself led him to that dis* ■ 
covery ? the merest novice in mathematics would, up- 
on this supposition, be equally qualified for the busi- 
ness of invention, with one that had made the greatest 
progress ; inasmuch as these general principles of the 
science are commonly alike known to both. But the 
truth of it is, Euclid, having found out angles, to which 
the three angles of a triangle, and two right angles, be- 
ing compared, were found severally equal : thereby as- 
certained the proposition in question, by showing it to 
terminate in the above axiom, though perhaps the ax- 
iom itself was never once thought of, during the whole 
course of the investigation. 



■^'34 ELEMENTS OF tOGIG. 

Sec. XXIV,... Reasoning, (hough resolvable into general 
truths, rests immediately upon particular self-evident 
propositions. 

And here it may not be improper to observe, that 
though it be usual in reasoning, when we arrive at any 
particular self-evident proposition, to refer to the gene- 
ral axiom under which it is comprehended : yet is not 
this done out of absolute necessity, or for the sake of 
any additional confirmation. All intuitive truths, whe^ 
ther general or particular, standing upon the same foun- 
dation of immediate perception, are necessarily em- 
braced for their own sake, and require no mutual illus- 
tration one from another. When, therefore, we have 
found, that the three angles of a triangle, and two right 
angles, are severally equal to the angles formed by one 
right line standing upon another, we thence immediate- 
ly discern their equality between themselves, indepen- 
dent of the general axiom into which this truth may be 
lesolved. Nor do we in reality refer to that axiom, by 
way of evidence and proof; but merely to show the 
coincidence of the example under notice, with a pre- 
viously established general principle. The same thing 
happens in all other demonstrations whatsoever, which, 
terminating thus in particular self-evident truths, are 
therefore of themselves sufficient to certainty, and ac- 
quire not any new force by being ultimately referred t# 
general maxims. This I mention here, to obviate a 
common prejudice, whence many are led to imagine, 
that particular intuitive propositions derive their evi- 
dence from those that are general, as being necessarily 
included in them. But since they both stand upon the 
same foundation of certainty, and are admitted in con- 
sequence of immediate perception, they have there- 
fore an equal claim to self-evidence, and cannot be 
made plainer by any mutual appeal. 

dkc. xxY.,... Particular Self-evident propositions so call' 
ed here, in opposition to general principles. 

As, however, it is usual in the method of science t© 
I'^j doyv|i certain general principles by way of fenac^^ 



ELEMENTS QF LOGIC. 335 

kon for our future reasonings ; some will perhaps ob- 
ject, that this seems to be a needless precaution, since 
demonstrations may subsist without them, and common- 
ly terminate in particular self-evident truths, peculiar- 
ly connected with the subject under consideration. la 
order, therefore, to give a distinct idea, of the true de- 
sign of this previous step, we shall begin with observ- 
ing, that by the particular propositions in which demon- 
strations terminate, must not be understood such as are 
so, according to the strict definition of the word, or ift 
opposition to universals ; but only confined and limited 
truths, when compared with others that are more gene- 
ral. Thus the proposition, circles, equal to one and the 
same circle, are equal between themselves, is, in strict- 
ness and propriety of speech, universal, because the 
subject is taken in its full extent, and the predicate 
agrees to all the individuals comprehended under it. 
We here, notwithstanding, consider it as only a partic- 
ular truth ; because it is of a very limited nature, whea 
compared with the general axiom mentioned above ; 
things equal to one and the same thing, are equal to one 
another. For this not only extends to all the various 
species of figures, but takes in every object without 
exception, that comes under the denomination of quan* 
tity. 

Sec. XXVI General Principles serve, firsts to Con- 
tract the bottom of our Reasoning. 

This point settled, it will easily appear, that the me- 
thod of premising general principles in the sciences 
answers these two great and valuable purposes. Firstf 
to contract the bottom of our reasoning, and bring it 
within such bounds as are sufficiently accommodated to 
the capicity of the mind. Por demonstrations being 
carried on by means of intermediate ideas, which must 
always have some peculiar connexion with the matter ia 
hand, the particular self-evident propositions in which 
they terminate, are almost as various as the subjects to 
which they relate. Thus in investigating the equality 
•f different objects, whether angles, triangles, circles, 
squares, k$« the intuitive truths^ on which the proofs 



236 e'lements op l&gic, 

resl, ahvays regard the particular species, and may be 
therefore multiplied, in infinitum, as well as the species 
themselves. But now it is remarkable, that all these 
several truths, numerous as they may appear, are j^et 
reducible to this one general principle already mention- 
ed ; things equal to one and the same thing are equal to 
one another. The same observation will be found to 
hold in other parts of human knowledge ; insomuch 
that though the particular truths, on which we bottom 
our reasonings, are really innumerable ; they yet may 
be all, without exception, resolved ipto a very few ge- 
neral maxims, and thereby brought readily within the 
compass of the understanding. When, therefore, we 
begin with premising these general truths, and as we 
advance in science, take care universally to resolve our 
demonstrations into them ; this must needs add a won- 
derful clearness and perspicuity to our reasonings, and 
by establishing them upon a foundation previously ad- 
mitted, and of whose strength and firmness we are 
abundantly satisfied, give them that irresistible force 
and influence, which serves to produce absolute certain- 
ty. Nor can we possibly imagine any thing more ele- 
gant and beautiful, than thus to behold knowledge ris- 
ing from a firm and fathomable root, bearing its head 
aloft, and spreading forth into innumerable branches of 
science ; which, though variously implicated and en- 
tangled, and stretching to a vast extent, yet by their 
union in one common slock, derive thence so sure and 
stable a support, that all the assaults of cavil and scep- 
ticism are not able to destroy or loosen their connexion. 

Sec. XXVII Secondly, to ascertain the Justness of it 

with more Ease, and less Hazard of Miscarriage. 

^ But, secondly, another purpose served by general 
principles is, that they enable us with less fatigue and 
labour and less hazard of miscarriage, to satisfy our- 
selves as to the justness of those reasonings by which 
science is established. For since demonstrations, when 
pursued to their source, terminate always in particular 
intuitive truths, which are therefore the ultimate foun° 
Nation of certainty ; it greatly improves us, to bev/are. 



i;lements of logic. 237 

that we receive not any propositions under this name, 
until we have distinctly settled them in our own mi-nds, 
and attained a full and clear perception of that self-evi- 
<ience, on account of which they are admitted without 
proof. But now these propositions being many in num- 
ber, and differing according to the nature of the subject 
about which our researches are employed ; it must great- 
ly perplex and retard our reasonings, were we to check 
©urselves every time they occur, in order to examine 
them by the rules of first principles. Nor is it a matter 
©f slight consideration, that in tli€ heat and hurry of 
demonstrating, while the mind is advancing eagerly 
from one discovery to another, we should be often 
tempted to pass them over hastily, and without that 
attention their importance requires ; which must ex- 
pose us to many errors and mistakes. These inconve- 
niences are effectually prevented by the method of pre- 
mising general truths : because upon referring particu- 
lar propositions to them, as the connexion is obvious at 
first sight, and cannot possibly escape our notice, the 
evidence is discerned to be the very same with that of 
the principles to. which they belong. And thus by a 
bare reference, without the trouble of particular ex- 
aminations, the grounds of reasoning are ascertained, 
and our demonstrations found, ultimately to rest on 
maxims previously established. 

Sec. XXVIII. ...O/' the manner of linking propositions 
together, in order to the forming of legitimate demon- 
atrations. 

Having explained the use of general principles, 
shown them to be the great media of certainty, and 
found, that in order to enlarge the bounds of science^ 
we must have recourse to intermediate ideas, as by 
means of them we are furnished with the several pre- 
vious truths, oi which reasoning consists ; it now re- 
mains, that we inquire in what manner these truths 
are to be disposed and linked together, towards the 
forming of just and legitimate demonstrations. We have 
seen already, in the preceding book, that syllogisms^ 
drawn up according to the rules there established, lead 



568 ELEMENTS OP h&m&, 

to a certain and infallible conclusion. If therefore evi- 
dent and allowed truths are disposed in a syllogisHc 
order, so as to offer a regular conclusion, that conclu- 
sion is necessarily true and valid. And since, in eve]*^ 
genuine syllogism, if the premises are true, the con- 
clusion must needs be true ; it manifestly follows, that 
the conclusion already gained, being now a known and 
established truth, may be admitted as one of the pre* 
mises of any succeeding syllogism, and thereby con- 
tribute towards the obtaining a new conclusion. In 
this manner may syllogisms follow one another in 
train, and lead to a successive discovery of truth ; care 
being always taken, that the premises, in every step, 
are either self-evident propositions, or conclusions pre- 
viously established. And indeed the whole art of demoti- 
atrating lies in this due and orderly combination of 
our syllogisms. For as by this means all the several 
premises made use of are manifestly true, all the seve- 
ral conclusions must be so too, and consequently the 
very last conclusion of the series, which is therefore 
said to be demonstrated. The same order is to be ob- 
served in the disposition of the demonstrations them- 
selves. That is, those propositions are always first to \w 
demonstrated, which furnish principles of reasoning in 
others ; it being upon the certainty of the principles 
made use of, that the certainty of the truths deduced 
from them depends. And since even the different 
branches and divisions of science have a near connex' 
ion among themselves, insomuch that the knowledge of 
one is often presupposed in another ; great care must 
be taken to adjust the several parts with an eye to this 
dependence, that those may always come first in or- 
der, whence \he pcshdaia of demonstration in others are 
borrowed. 

Sec. XXIX,. .Why the method here explained is called the 
method of science. 

In this way of putting together our thoughts, it is 
evident at first si?:ht, that however far we carry our re» 
searches, science md certainly will still attend us. But 
what is particularly elegant and happy in the method 



ELEMENTS OF LOGIC. 239 

HdVT explained, we hereby see knowledge rising out 
of its first elements, and discern distinctly how those 
elements are combined and interwoven, in order to the 
■erecting a goodly structure of truth. Experience fur- 
nishes us with simple ideas and their names which are 
the primary materials of thinking and communication. 
Definitions teach how to unite and bind these ideas to- 
gether, so as to form them into complex notions of va- 
rious orders and degrees. The general principles pre- 
mised in science exliibit to the understanding such in- 
tuitive and fundamental truths, as express the imme- 
diate relations between our ideas, and constitute the 
ultimate ground of,, certainty. Demonstrations link 
known and established truths together in such manner, 
that they necessarily lead to others which are unknown 
and remote. In fine, the duly adjusting the several 
branches of science, and the demonstrations in every 
branch, lays knowledge so open to the mind, that we 
see the parts of it growing one out of another, and cm- 
brace them with full conviction and assurance. Thus 
are we gradually led from simple ideas, through all the 
windings and labyrinths of truth, until we at length 
reach the highest and most exalted discoveries of hu- 
m^n reason. It is true, the method here laid down hath 
hitherto been observed strictly only among mathemati- 
cians ; and is therefore by many thought to be peculiar 
to number and magnitude. But it appears evidently 
from what we have said above, that it may be equally 
applied in all such other parts of knowledge as regard 
the abstract ideas of the mind, and the relations sub- 
sisting between them. And since, wherever it is ap- 
plied, it necessarily begets science and certainty, we 
have hence chosen to denominate it the method of 
science, the better to intimate its true nature and ex- 
tent. 



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